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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 (12991a  - 15088a b - 12689a*b  + 7348b  - 1905a c + 5604a*b*c +
     ------------------------------------------------------------------------
           2            2           2         3        2               
     15675b c + 10075a*c  + 11111b*c  + 15160c  + 6703a d - 7938a*b*d +
     ------------------------------------------------------------------------
           2                                 2            2           2  
     13006b d - 1090a*c*d - 6780b*c*d + 1960c d + 15919a*d  + 15575b*d  -
     ------------------------------------------------------------------------
            2         3         2                      2                
     3537c*d  + 14739d  + 15196a e + 8999a*b*e + 10283b e - 11117a*c*e +
     ------------------------------------------------------------------------
                        2                                               2   
     14710b*c*e + 14249c e + 12115a*d*e - 2345b*d*e - 3658c*d*e - 10666d e -
     ------------------------------------------------------------------------
             2          2           2           2         3       3       2 
     12042a*e  - 2396b*e  - 14870c*e  - 11274d*e  - 12869e , - 89a  - 793a b
     ------------------------------------------------------------------------
              2         3        2                      2           2  
     - 9850a*b  - 12073b  + 5819a c + 4929a*b*c + 12697b c - 7203a*c  +
     ------------------------------------------------------------------------
             2         3        2                    2               
     11349b*c  - 10804c  - 7979a d + 7993a*b*d - 190b d - 2062a*c*d +
     ------------------------------------------------------------------------
                      2            2           2           2        3  
     2946b*c*d + 4970c d + 15069a*d  + 14667b*d  - 10518c*d  - 3855d  -
     ------------------------------------------------------------------------
          2                    2                                  2   
     3957a e - 78a*b*e + 13048b e - 7114a*c*e + 10333b*c*e - 2198c e +
     ------------------------------------------------------------------------
                                               2           2          2  
     9382a*d*e + 8940b*d*e + 4477c*d*e - 15008d e + 5582a*e  + 5253b*e  +
     ------------------------------------------------------------------------
            2           2        3       3        2           2       3  
     4900c*e  - 11199d*e  + 8926e , 3146a  + 4259a b + 2247a*b  - 978b  +
     ------------------------------------------------------------------------
          2                      2            2          2         3  
     7136a c + 1436a*b*c - 15795b c + 13761a*c  + 4245b*c  + 14036c  -
     ------------------------------------------------------------------------
          2                     2                                  2   
     4644a d + 9012a*b*d - 1735b d + 3134a*c*d + 11304b*c*d + 3962c d -
     ------------------------------------------------------------------------
            2           2           2       3         2               
     9940a*d  + 10348b*d  + 12103c*d  - 877d  + 11945a e - 8548a*b*e -
     ------------------------------------------------------------------------
          2                                 2                            
     5280b e - 1517a*c*e - 2852b*c*e - 1426c e - 8591a*d*e - 12681b*d*e -
     ------------------------------------------------------------------------
                        2           2          2         2          2  
     10937c*d*e + 12683d e + 3782a*e  - 1035b*e  + 684c*e  + 5969d*e  -
     ------------------------------------------------------------------------
           3
     12932e )

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+2788b3-2236a2c+8481abc+11017b2c+2081ac2-6462bc2-13872c3+10185a2d-
     ------------------------------------------------------------------------
     15708abd+13210b2d+2763acd+8155bcd+2311c2d+2984ad2-11924bd2-14514cd2+
     ------------------------------------------------------------------------
     7188d3-2394a2e+10422abe-7085b2e+1063ace-6784bce+5293c2e+15791ade-6207bde
     ------------------------------------------------------------------------
     +7982cde-4571d2e-6725ae2+8500be2+13779ce2+15697de2+7005e3
     ------------------------------------------------------------------------
     a2b+9171b3-162a2c+7112abc+7672b2c-8182ac2-8333bc2+15921c3-4838a2d+
     ------------------------------------------------------------------------
     3876abd-450b2d+11061acd-11705bcd+7314c2d+8493ad2+9178bd2+8965cd2-2803d3+
     ------------------------------------------------------------------------
     11416a2e-1455abe-8719b2e+12439ace+11373bce+3840c2e-7652ade-9348bde+
     ------------------------------------------------------------------------
     11565cde+13357d2e-11622ae2-14922be2-9337ce2+6797de2+4689e3
     ------------------------------------------------------------------------
     a3+9000b3+3609a2c+7661abc-13072b2c+15271ac2+13314bc2-9922c3+10555a2d+
     ------------------------------------------------------------------------
     4449abd-11746b2d-8422acd-2528bcd-14267c2d+10304ad2-13976bd2-6344cd2-
     ------------------------------------------------------------------------
     8908d3+15851a2e+2997abe+3699b2e-4019ace+6426bce+654c2e-7514ade-7635bde-
     ------------------------------------------------------------------------
     9866cde+3731d2e-9115ae2-9196be2-14291ce2+7065de2-5211e3
     ------------------------------------------------------------------------
     b3c+3747a2c2+6161abc2+8654b2c2-11003ac3-8507bc3+1001c4-37b3d-13758a2cd+
     ------------------------------------------------------------------------
     1997abcd-14442b2cd+5193ac2d-12982bc2d-12262c3d-7257a2d2-12293abd2+
     ------------------------------------------------------------------------
     990b2d2+4879acd2-3387bcd2-15551c2d2-9690ad3+204bd3-10656cd3-10697d4-
     ------------------------------------------------------------------------
     8375b3e+12615a2ce+12274abce+13137b2ce-12768ac2e-9301bc2e-249c3e-5342a2de
     ------------------------------------------------------------------------
     -13464abde-11451b2de+14327acde-11532bcde+1985c2de+13167ad2e+153bd2e-
     ------------------------------------------------------------------------
     4980cd2e+6890d3e-8559a2e2+7884abe2-1336b2e2-6774ace2+10430bce2-12655c2e2
     ------------------------------------------------------------------------
     +8834ade2+1362bde2-5320cde2+5051d2e2-1793ae3-5948be3-1094ce3-1312de3-
     ------------------------------------------------------------------------
     11584e4 b4-4411a2c2+160abc2+1671b2c2-14844ac3+921bc3+7014c4+15103b3d-
     ------------------------------------------------------------------------
     10710a2cd-5955abcd-1113b2cd-3425ac2d-12938bc2d+7211c3d-12515a2d2+
     ------------------------------------------------------------------------
     6517abd2-2859b2d2-3273acd2-3526bcd2-4566c2d2-8450ad3+5408bd3-11301cd3+
     ------------------------------------------------------------------------
     114d4+2806b3e+6502a2ce+5815abce+11702b2ce+12568ac2e-12176bc2e+12953c3e-
     ------------------------------------------------------------------------
     4864a2de+13953abde+10143b2de-2690acde+14235bcde-2397c2de+10969ad2e+
     ------------------------------------------------------------------------
     3312bd2e-3314cd2e-11673d3e+2649a2e2+15671abe2+2777b2e2-9292ace2+5349bce2
     ------------------------------------------------------------------------
     +4423c2e2-4923ade2+3507bde2+10257cde2+12858d2e2-987ae3-13056be3-1714ce3-
     ------------------------------------------------------------------------
     13008de3-4365e4 abc3-9961b2c3-8779ac4+1032bc4-12899c5+5402a2c2d-
     ------------------------------------------------------------------------
     9434abc2d-9047b2c2d-8071ac3d-5840bc3d-12598c4d+8629b3d2-407a2cd2+
     ------------------------------------------------------------------------
     7559abcd2+13330b2cd2+13705ac2d2+10056bc2d2+6744c3d2-11476a2d3-1572abd3-
     ------------------------------------------------------------------------
     12755b2d3+2707acd3-9972bcd3+14386c2d3+1757ad4+5402bd4-14857cd4-5114d5-
     ------------------------------------------------------------------------
     2727a2c2e+15424abc2e-839b2c2e-160ac3e+7638bc3e-3118c4e+8455b3de-
     ------------------------------------------------------------------------
     15809a2cde-5488abcde+7428b2cde-605ac2de-13754bc2de+9930c3de-15563a2d2e+
     ------------------------------------------------------------------------
     5827abd2e+14058b2d2e+13675acd2e+14057bcd2e+2054c2d2e+12287ad3e-8484bd3e-
     ------------------------------------------------------------------------
     4998cd3e-1156d4e+4145b3e2+7325a2ce2-4298abce2+1122b2ce2+12016ac2e2+
     ------------------------------------------------------------------------
     2317bc2e2+11111c3e2-5656a2de2+12714abde2-7657b2de2+393acde2-359bcde2+
     ------------------------------------------------------------------------
     3059c2de2+1451ad2e2-4472bd2e2-6402cd2e2-7636d3e2-5057a2e3-15848abe3+
     ------------------------------------------------------------------------
     8787b2e3+10578ace3+12334bce3+7331c2e3-9369ade3+3800bde3-2560cde3+
     ------------------------------------------------------------------------
     5359d2e3+9032ae4-10893be4-4871ce4+9611de4-12978e5
     ------------------------------------------------------------------------
     a2c3-14592b2c3-365ac4-4564bc4+10691c5-9460a2c2d-12775abc2d-8450b2c2d+
     ------------------------------------------------------------------------
     5144ac3d+13592bc3d-8337c4d+1270b3d2+14935a2cd2-8882abcd2-4151b2cd2+
     ------------------------------------------------------------------------
     3229ac2d2-13043bc2d2-9549c3d2-14550a2d3+8729abd3-9019b2d3+14248acd3+
     ------------------------------------------------------------------------
     5904bcd3-1680c2d3+11283ad4+10280bd4+5309cd4+5473d5+922a2c2e+3355abc2e-
     ------------------------------------------------------------------------
     7454b2c2e+10905ac3e+15801bc3e-7377c4e-5318b3de-7568a2cde+7702abcde+
     ------------------------------------------------------------------------
     835b2cde-9189ac2de+11500bc2de-16000c3de-8130a2d2e-2221abd2e+4316b2d2e-
     ------------------------------------------------------------------------
     7598acd2e+9331bcd2e-2306c2d2e-7921ad3e+7465bd3e-13222cd3e+11014d4e+
     ------------------------------------------------------------------------
     14788b3e2+3555a2ce2+4271abce2+3893b2ce2+851ac2e2+8543bc2e2+12218c3e2+
     ------------------------------------------------------------------------
     3257a2de2-2971abde2-9932b2de2+1642acde2+4373bcde2-777c2de2+3972ad2e2+
     ------------------------------------------------------------------------
     675bd2e2-8779cd2e2-566d3e2-2608a2e3+11953abe3-14351b2e3-5027ace3-
     ------------------------------------------------------------------------
     14586bce3-5767c2e3+13208ade3-6629bde3+1967cde3-7801d2e3+4526ae4-15305be4
     ------------------------------------------------------------------------
     -6402ce4+6153de4-10036e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R