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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 (5529a  + 11090a b + 7559a*b  + 9668b  + 10339a c - 6499a*b*c -
     ------------------------------------------------------------------------
          2            2           2         3        2                
     7454b c + 11521a*c  + 12186b*c  + 12476c  + 9987a d + 11364a*b*d +
     ------------------------------------------------------------------------
          2                                   2           2           2  
     1147b d - 2995a*c*d + 10986b*c*d + 10228c d - 4197a*d  - 15879b*d  +
     ------------------------------------------------------------------------
            2        3        2                     2                
     6456c*d  - 5940d  + 8961a e - 8135a*b*e - 5803b e + 15415a*c*e -
     ------------------------------------------------------------------------
                       2                                               2   
     12468b*c*e + 9641c e + 11709a*d*e - 3311b*d*e + 6983c*d*e - 11010d e -
     ------------------------------------------------------------------------
             2           2           2          2         3          3  
     15231a*e  - 14353b*e  - 11934c*e  + 3749d*e  + 14512e , - 10874a  -
     ------------------------------------------------------------------------
          2           2        3         2                      2          2
     6375a b - 6925a*b  + 8026b  + 11738a c - 4837a*b*c + 13492b c - 635a*c 
     ------------------------------------------------------------------------
              2        3       2                    2                
     - 9746b*c  + 9338c  + 433a d - 93a*b*d + 12396b d + 10566a*c*d -
     ------------------------------------------------------------------------
                      2            2          2          2         3  
     148b*c*d - 14305c d + 10268a*d  - 5599b*d  - 8194c*d  - 14448d  -
     ------------------------------------------------------------------------
          2                      2                                  2   
     4538a e + 6540a*b*e - 11556b e - 1446a*c*e + 6065b*c*e + 11762c e -
     ------------------------------------------------------------------------
                                              2           2           2  
     5307a*d*e + 3833b*d*e + 792c*d*e - 15468d e - 1742a*e  - 10037b*e  -
     ------------------------------------------------------------------------
            2          2        3         3         2           2        3  
     5264c*e  - 3353d*e  + 7003e , - 7658a  + 11015a b + 6039a*b  + 1308b  +
     ------------------------------------------------------------------------
           2                     2           2          2         3  
     15207a c + 101a*b*c - 12995b c - 9459a*c  + 1561b*c  + 11240c  +
     ------------------------------------------------------------------------
           2                       2                                  2   
     11740a d - 12173a*b*d - 13147b d - 11327a*c*d + 4271b*c*d - 3601c d -
     ------------------------------------------------------------------------
             2          2          2         3        2               
     13133a*d  + 7594b*d  + 7386c*d  + 15507d  - 7251a e - 1364a*b*e -
     ------------------------------------------------------------------------
          2                                   2                           
     8637b e - 14239a*c*e - 7450b*c*e + 14069c e + 7708a*d*e - 9502b*d*e +
     ------------------------------------------------------------------------
                        2           2          2           2          2  
     10871c*d*e + 10978d e + 4433a*e  - 7975b*e  - 10165c*e  + 1382d*e  -
     ------------------------------------------------------------------------
          3
     3644e )

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 = | ab2-3112b3-679a2c+13021abc+4803b2c+15467ac2-1745bc2+13925c3-1507a2d-
     ------------------------------------------------------------------------
     3679abd-14621b2d+6798acd+7649bcd-8726c2d+4088ad2+5716bd2+15624cd2-3906d3
     ------------------------------------------------------------------------
     -4897a2e+15423abe-14955b2e+14070ace-12566bce+14433c2e-11308ade+15938bde+
     ------------------------------------------------------------------------
     1849cde+8500d2e+8794ae2+7019be2-10095ce2-258de2-7739e3
     ------------------------------------------------------------------------
     a2b-12741b3-1518a2c+1538abc+10100b2c+15170ac2+4524bc2+3207c3+12046a2d-
     ------------------------------------------------------------------------
     4563abd-9318b2d+10163acd+14065bcd+14758c2d-1210ad2-7081bd2-1234cd2+
     ------------------------------------------------------------------------
     4561d3+10117a2e-4234abe-15950b2e-7848ace-8251bce-6607c2e-3835ade-
     ------------------------------------------------------------------------
     12008bde+9305cde-13788d2e-1065ae2-11473be2-1020ce2-7160de2-8239e3
     ------------------------------------------------------------------------
     a3-10989b3-3214a2c-4102abc+4760b2c-11274ac2-4180bc2-10025c3+3027a2d-
     ------------------------------------------------------------------------
     9559abd-12118b2d-9791acd+8756bcd-8918c2d+15840ad2-4780bd2+298cd2+15940d3
     ------------------------------------------------------------------------
     -10835a2e+7531abe+4858b2e-8921ace+9955bce+8166c2e+2687ade+1207bde+
     ------------------------------------------------------------------------
     10390cde-15287d2e-4761ae2+1901be2+3169ce2-8137de2-13866e3
     ------------------------------------------------------------------------
     b3c-9157a2c2-14843abc2-6724b2c2+11671ac3-12678bc3+4793c4-5801b3d-
     ------------------------------------------------------------------------
     8918a2cd+10852abcd-12852b2cd+12954ac2d-12969bc2d-5609c3d+7706a2d2+
     ------------------------------------------------------------------------
     5562abd2+1732b2d2+930acd2+15431bcd2-3976c2d2+6953ad3+6332bd3-11132cd3+
     ------------------------------------------------------------------------
     10273d4+13294b3e-8708a2ce+2041abce-7424b2ce+5800ac2e-1901bc2e-11382c3e+
     ------------------------------------------------------------------------
     816a2de+13540abde+5617b2de-11217acde+5826bcde+12827c2de+15624ad2e+
     ------------------------------------------------------------------------
     10123bd2e+4085cd2e+5155d3e+5335a2e2-4930abe2+9865b2e2-14705ace2-2994bce2
     ------------------------------------------------------------------------
     +14936c2e2+12042ade2-14339bde2+15880cde2-2763d2e2+5243ae3-4945be3-
     ------------------------------------------------------------------------
     4208ce3+1642de3-8381e4 b4+15345a2c2+11088abc2-8008b2c2-11021ac3-491bc3-
     ------------------------------------------------------------------------
     4693c4-4542b3d+7259a2cd-8689abcd-10439b2cd-10262ac2d+4531bc2d+14808c3d-
     ------------------------------------------------------------------------
     3085a2d2+14450abd2+12318b2d2-12039acd2+7509bcd2-780c2d2-3795ad3+9059bd3-
     ------------------------------------------------------------------------
     12743cd3+144d4-12021b3e-11137a2ce-6024abce+137b2ce-1132ac2e-2629bc2e-
     ------------------------------------------------------------------------
     9593c3e-6133a2de-15177abde+15684b2de+4073acde+1572bcde-8303c2de+1312ad2e
     ------------------------------------------------------------------------
     +13503bd2e-15183cd2e-6150d3e+2054a2e2+15040abe2-12365b2e2+2960ace2-
     ------------------------------------------------------------------------
     13469bce2-2994c2e2+13113ade2-5800bde2+6452cde2-8415d2e2+12338ae3+3449be3
     ------------------------------------------------------------------------
     -1134ce3+4907de3+4740e4
     ------------------------------------------------------------------------
     abc3-7873b2c3+3165ac4-2471bc4+15225c5+14352a2c2d+14980abc2d-10061b2c2d+
     ------------------------------------------------------------------------
     8538ac3d-9878bc3d+7229c4d-3765b3d2+1155a2cd2-14758abcd2-2310b2cd2+
     ------------------------------------------------------------------------
     7726ac2d2-1860bc2d2+6917c3d2-15928a2d3+5123abd3+3664b2d3+1241acd3+
     ------------------------------------------------------------------------
     8095bcd3+2060c2d3-9420ad4-2720bd4+584cd4+5520d5+1735a2c2e-7598abc2e-
     ------------------------------------------------------------------------
     9067b2c2e+1978ac3e-5772bc3e+791c4e-9975b3de+15685a2cde-10231abcde-
     ------------------------------------------------------------------------
     4747b2cde+10530ac2de-3896bc2de-4469c3de-2838a2d2e-3564abd2e-7208b2d2e+
     ------------------------------------------------------------------------
     9062acd2e+3571bcd2e+1964c2d2e+9894ad3e-2916bd3e-5205cd3e+4287d4e+
     ------------------------------------------------------------------------
     15977b3e2-3376a2ce2+3016abce2+6245b2ce2-3922ac2e2-9549bc2e2+513c3e2+
     ------------------------------------------------------------------------
     4941a2de2-9918abde2+517b2de2+7285acde2-3728bcde2+6c2de2-12641ad2e2-
     ------------------------------------------------------------------------
     14118bd2e2+10549cd2e2+12319d3e2+4765a2e3+2733abe3+13414b2e3-14915ace3+
     ------------------------------------------------------------------------
     11696bce3+9917c2e3-11172ade3-2056bde3-15345cde3+14478d2e3+9542ae4+
     ------------------------------------------------------------------------
     2466be4-11315ce4-15225de4+5926e5
     ------------------------------------------------------------------------
     a2c3+1903b2c3+12990ac4-14323bc4-10459c5+13917a2c2d-11400abc2d-5087b2c2d+
     ------------------------------------------------------------------------
     10716ac3d+15620bc3d+2368c4d+2370b3d2+4620a2cd2+12045abcd2-3701b2cd2+
     ------------------------------------------------------------------------
     452ac2d2-6097bc2d2-11924c3d2+15666a2d3-8762abd3-5698b2d3-9592acd3+
     ------------------------------------------------------------------------
     10751bcd3+14132c2d3+2765ad4+8492bd4-550cd4-10638d5-7726a2c2e+121abc2e+
     ------------------------------------------------------------------------
     4353b2c2e+15347ac3e-8708bc3e-11343c4e-7593b3de-8790a2cde+6953abcde+
     ------------------------------------------------------------------------
     12588b2cde+11270ac2de-2079bc2de-2173c3de-8333a2d2e-2883abd2e-12138b2d2e+
     ------------------------------------------------------------------------
     6842acd2e+10937bcd2e-10444c2d2e+13237ad3e-9314bd3e-320cd3e+9392d4e+
     ------------------------------------------------------------------------
     13059b3e2-5423a2ce2-1342abce2-2427b2ce2+7019ac2e2+7573bc2e2-3774c3e2-
     ------------------------------------------------------------------------
     9428a2de2+6891abde2-14142b2de2-9111acde2-13887bcde2-6118c2de2-9388ad2e2+
     ------------------------------------------------------------------------
     12790bd2e2+4842cd2e2+6743d3e2-274a2e3-10591abe3-9833b2e3+2652ace3+
     ------------------------------------------------------------------------
     12572bce3-7935c2e3+10080ade3+8499bde3+11929cde3-7629d2e3-4499ae4+9368be4
     ------------------------------------------------------------------------
     -5245ce4+10078de4+5385e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R