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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 (4477a  + 4256a b - 11467a*b  - 1063b  + 7023a c - 7933a*b*c -
     ------------------------------------------------------------------------
           2           2          2        3         2               
     13211b c + 8756a*c  + 8478b*c  - 2104c  + 10534a d + 4238a*b*d +
     ------------------------------------------------------------------------
           2                                   2           2           2  
     10063b d - 13554a*c*d - 2762b*c*d - 15012c d - 8452a*d  + 14687b*d  -
     ------------------------------------------------------------------------
           2        3         2                    2                
     148c*d  - 6760d  + 15702a e - 202a*b*e - 1471b e + 14236a*c*e +
     ------------------------------------------------------------------------
                        2                                               2   
     13481b*c*e - 15084c e + 8143a*d*e - 11924b*d*e - 6012c*d*e - 10233d e +
     ------------------------------------------------------------------------
            2          2           2          2      3      3         2   
     3781a*e  - 5527b*e  - 10199c*e  + 1076d*e  + 17e , - 2a  + 15349a b +
     ------------------------------------------------------------------------
            2        3        2                       2           2  
     4612a*b  - 3458b  + 7468a c + 10846a*b*c - 13871b c + 1682a*c  -
     ------------------------------------------------------------------------
            2         3        2                      2               
     1455b*c  - 14929c  + 8100a d - 4943a*b*d - 10596b d - 4189a*c*d -
     ------------------------------------------------------------------------
                       2           2          2          2         3  
     13701b*c*d - 3209c d + 1381a*d  + 2014b*d  + 6716c*d  + 10968d  +
     ------------------------------------------------------------------------
           2                      2                                  2   
     11309a e - 5129a*b*e - 15129b e + 10934a*c*e - 2319b*c*e + 6296c e +
     ------------------------------------------------------------------------
                                                2           2           2  
     7694a*d*e + 3103b*d*e - 13842c*d*e + 13221d e - 9116a*e  - 15004b*e  +
     ------------------------------------------------------------------------
            2          2        3        3         2            2         3  
     6880c*e  + 2501d*e  + 9825e , 15183a  - 15693a b + 13790a*b  + 13750b  -
     ------------------------------------------------------------------------
          2                       2           2           2        3  
     6626a c + 14541a*b*c + 14465b c - 8704a*c  - 11680b*c  + 1297c  -
     ------------------------------------------------------------------------
          2                       2                                   2   
     6580a d - 14972a*b*d + 12541b d - 3715a*c*d + 10507b*c*d + 13528c d -
     ------------------------------------------------------------------------
             2           2           2        3        2               
     15572a*d  + 12334b*d  + 13281c*d  + 4174d  - 6955a e + 9437a*b*e -
     ------------------------------------------------------------------------
           2                                  2                            
     13492b e + 6790a*c*e + 10306b*c*e + 6104c e - 2973a*d*e + 14042b*d*e -
     ------------------------------------------------------------------------
                      2           2           2           2          2  
     9423c*d*e - 1783d e - 4478a*e  - 14838b*e  + 10939c*e  + 9384d*e  -
     ------------------------------------------------------------------------
           3
     11223e )

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 = | ab2-13741b3-15042a2c-12837abc-11797b2c+4534ac2+1576bc2+5968c3+12367a2d
     ------------------------------------------------------------------------
     -9691abd-14672b2d+11385acd-3988bcd-5621c2d+6083ad2-462bd2+14100cd2-
     ------------------------------------------------------------------------
     8938d3-15832a2e-1364abe+4801b2e+7783ace-6118bce+6167c2e+12870ade+1357bde
     ------------------------------------------------------------------------
     +111cde-10595d2e-14372ae2-10081be2+1205ce2-8562de2+7754e3
     ------------------------------------------------------------------------
     a2b-495b3-7114a2c+11519abc-8074b2c-14831ac2-7831bc2+7985c3+13928a2d+
     ------------------------------------------------------------------------
     6291abd-5370b2d-11947acd+7969bcd+13086c2d+15914ad2+4439bd2+8345cd2+
     ------------------------------------------------------------------------
     12632d3-8134a2e-12190abe+839b2e-9544ace-9203bce-8194c2e-10547ade-2158bde
     ------------------------------------------------------------------------
     -11227cde-142d2e-368ae2+3533be2-8279ce2-421de2+9300e3
     ------------------------------------------------------------------------
     a3-8569b3+1391a2c-10492abc+15500b2c-12258ac2-10734bc2+3520c3-5a2d+
     ------------------------------------------------------------------------
     12875abd+6636b2d+14788acd-4259bcd-12115c2d+1937ad2-10368bd2-14108cd2+
     ------------------------------------------------------------------------
     617d3-1355a2e+2090abe+11935b2e-2113ace+8572bce+9664c2e-15774ade-8622bde+
     ------------------------------------------------------------------------
     13329cde-6067d2e+9882ae2-13640be2-4200ce2+1967de2+8296e3
     ------------------------------------------------------------------------
     b3c+15168a2c2+1526abc2-1080b2c2+2769ac3-9863bc3-13142c4+15878b3d-
     ------------------------------------------------------------------------
     7835a2cd-782abcd-1063b2cd+2796ac2d-3703bc2d-1929c3d-1706a2d2+11566abd2+
     ------------------------------------------------------------------------
     12103b2d2+8279acd2-13800bcd2+12191c2d2+14424ad3+1063bd3-7141cd3+15090d4+
     ------------------------------------------------------------------------
     13091b3e-13470a2ce+8135abce-1625b2ce+8546ac2e-13427bc2e-7036c3e+819a2de+
     ------------------------------------------------------------------------
     14226abde-1159b2de+1301acde+6863bcde-15313c2de+4748ad2e-2546bd2e-
     ------------------------------------------------------------------------
     11607cd2e-3011d3e+4567a2e2+6754abe2+8995b2e2+13975ace2+9744bce2-
     ------------------------------------------------------------------------
     12366c2e2-9657ade2-12708bde2-1072cde2-9213d2e2+12079ae3+1136be3+2539ce3-
     ------------------------------------------------------------------------
     137de3-2504e4 b4+7503a2c2+8944abc2+8903b2c2+2646ac3-4377bc3-8785c4+
     ------------------------------------------------------------------------
     15145b3d-4864a2cd+6424abcd-12932b2cd+1133ac2d-13693bc2d-11188c3d+
     ------------------------------------------------------------------------
     13342a2d2+9611abd2-8977b2d2+6486acd2-13043bcd2-5860c2d2+7533ad3-7936bd3-
     ------------------------------------------------------------------------
     6633cd3+6602d4-5100b3e+3302a2ce-5888abce+7328b2ce+9193ac2e+12931bc2e+
     ------------------------------------------------------------------------
     7521c3e+4710a2de+5059abde+9197b2de+9669acde-11083bcde-2297c2de-5949ad2e+
     ------------------------------------------------------------------------
     13545bd2e-7208cd2e+14621d3e+13267a2e2-9031abe2-9159b2e2+11299ace2-
     ------------------------------------------------------------------------
     7860bce2-11726c2e2-1936ade2+15951bde2-9616cde2+1374d2e2+13438ae3+
     ------------------------------------------------------------------------
     10846be3+15029ce3+934de3+10533e4
     ------------------------------------------------------------------------
     abc3+13314b2c3+7382ac4+6426bc4+11365c5+13175a2c2d+12155abc2d+8066b2c2d+
     ------------------------------------------------------------------------
     7880ac3d-5516bc3d+10681c4d-5869b3d2-2271a2cd2-2656abcd2-9411b2cd2-
     ------------------------------------------------------------------------
     15240ac2d2+392bc2d2+10194c3d2+5189a2d3+211abd3-12486b2d3+13108acd3-
     ------------------------------------------------------------------------
     4352bcd3-3074c2d3-11070ad4-8969bd4+15762cd4-5994d5-7089a2c2e+11503abc2e-
     ------------------------------------------------------------------------
     3177b2c2e-516ac3e+1902bc3e+8418c4e-13250b3de-7085a2cde-2538abcde-
     ------------------------------------------------------------------------
     163b2cde-975ac2de+2575bc2de+11929c3de+15480a2d2e+3399abd2e+11799b2d2e-
     ------------------------------------------------------------------------
     11698acd2e+8532bcd2e+1499c2d2e-10082ad3e-15653bd3e-14090cd3e+4043d4e+
     ------------------------------------------------------------------------
     6046b3e2-9951a2ce2-5475abce2+4705b2ce2+6629ac2e2-1123bc2e2-8038c3e2+
     ------------------------------------------------------------------------
     8583a2de2+11364abde2-8970b2de2+5033acde2-9229bcde2+5180c2de2+12834ad2e2-
     ------------------------------------------------------------------------
     15341bd2e2-209cd2e2+4547d3e2-8117a2e3+15024abe3+6085b2e3+7851ace3-
     ------------------------------------------------------------------------
     10463bce3+8760c2e3+13111ade3-3391bde3-5104cde3-3839d2e3+6207ae4-11768be4
     ------------------------------------------------------------------------
     +6869ce4-6369de4-8717e5
     ------------------------------------------------------------------------
     a2c3+13859b2c3-8485ac4+5944bc4-1808c5+12398a2c2d-14135abc2d+12608b2c2d+
     ------------------------------------------------------------------------
     13848ac3d+15947bc3d+11852c4d+13160b3d2-6157a2cd2+3258abcd2-8842b2cd2+
     ------------------------------------------------------------------------
     13615ac2d2+4056bc2d2-4638c3d2+4511a2d3-14401abd3-9226b2d3-5667acd3+
     ------------------------------------------------------------------------
     2186bcd3+10785c2d3-8363ad4-1353bd4-13530cd4+9868d5+4628a2c2e+14332abc2e+
     ------------------------------------------------------------------------
     10409b2c2e-14173ac3e-14259bc3e+11057c4e-527b3de+2785a2cde+11313abcde+
     ------------------------------------------------------------------------
     7065b2cde+6151ac2de+4104bc2de+634c3de-9791a2d2e+11294abd2e+3265b2d2e-
     ------------------------------------------------------------------------
     2275acd2e+7701bcd2e-729c2d2e-15594ad3e-12688bd3e-13185cd3e+3601d4e-
     ------------------------------------------------------------------------
     7020b3e2+9416a2ce2-1917abce2+1525b2ce2-13325ac2e2+14318bc2e2-14365c3e2+
     ------------------------------------------------------------------------
     128a2de2+8504abde2-10480b2de2+3748acde2+3616bcde2-8604c2de2-5998ad2e2-
     ------------------------------------------------------------------------
     7879bd2e2-7859cd2e2-782d3e2-8239a2e3+6538abe3+7392b2e3+11541ace3-
     ------------------------------------------------------------------------
     4088bce3-10175c2e3+3376ade3-15914bde3+8642cde3+368d2e3+15658ae4+10308be4
     ------------------------------------------------------------------------
     -14932ce4+3755de4+13596e5 |

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

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R