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];
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i2 : I = ideal(random(3,R),random(3,R),random(3,R))
3 2 2 3 2
o2 = ideal (7630a - 6236a b - 6486a*b - 431b - 4083a c + 15211a*b*c -
------------------------------------------------------------------------
2 2 2 3 2 2
6919b c - 5596a*c - 13887b*c - 2913c + 12074a d + 909a*b*d + 1130b d
------------------------------------------------------------------------
2 2 2 2
+ 4803a*c*d + 14872b*c*d - 13723c d + 10006a*d - 8108b*d + 5183c*d +
------------------------------------------------------------------------
3 2 2 2
9141d + 9a e + 11330a*b*e - 15295b e + 6867a*c*e - 6941b*c*e + 9627c e
------------------------------------------------------------------------
2 2 2
- 11482a*d*e - 8767b*d*e + 3076c*d*e - 14337d e + 2121a*e - 6867b*e +
------------------------------------------------------------------------
2 2 3 3 2 2 3
4287c*e + 9613d*e + 8130e , - 13304a + 14456a b - 6439a*b - 8710b -
------------------------------------------------------------------------
2 2 2 2 3 2
527a c - 10333a*b*c + 351b c + 14931a*c + 15376b*c + 9127c + 1585a d
------------------------------------------------------------------------
2 2 2
- 2081a*b*d + 648b d - 2472a*c*d - 9108b*c*d + 10080c d - 4985a*d +
------------------------------------------------------------------------
2 2 3 2 2
14377b*d - 1358c*d + 8319d - 5232a e - 6224a*b*e - 14024b e -
------------------------------------------------------------------------
2
12088a*c*e + 13501b*c*e + 14699c e + 1555a*d*e + 4781b*d*e + 925c*d*e +
------------------------------------------------------------------------
2 2 2 2 2 3 3
4486d e + 7064a*e - 9763b*e - 6945c*e + 104d*e - 4940e , - 14973a -
------------------------------------------------------------------------
2 2 3 2 2
7036a b - 3145a*b + 3553b - 11750a c + 14967a*b*c - 15864b c +
------------------------------------------------------------------------
2 2 3 2 2
13884a*c + 3249b*c + 2930c + 4149a d + 11506a*b*d - 2796b d +
------------------------------------------------------------------------
2 2 2 2
1833a*c*d - 4199b*c*d - 11381c d + 10431a*d - 7141b*d - 5161c*d +
------------------------------------------------------------------------
3 2 2
5017d - 14329a e - 3614a*b*e + 2704b e - 5387a*c*e - 1865b*c*e -
------------------------------------------------------------------------
2 2 2
12569c e - 11747a*d*e + 11922b*d*e + 10238c*d*e - 4387d e - 7435a*e -
------------------------------------------------------------------------
2 2 2 3
7170b*e - 10590c*e - 15354d*e - 6025e )
o2 : Ideal of R
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i3 : gens gb(I,PairLimit=>7);
1 7
o3 : Matrix R <--- R
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Get the Groebner basis object:
i4 : g = gb(I,StopBeforeComputation => true);
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i5 : leadTerm gens g
o5 = | ab2 a2b a3 b3c b4 abc3 a2c3 |
1 7
o5 : Matrix R <--- R
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We can make a Groebner basis snapshot by using StopBeforeComputation, or
gbSnapshot:
i6 : gens gb(I,StopBeforeComputation => true)
o6 = | ab2-8237b3+10973a2c+7857abc-1443b2c-2468ac2+320bc2+5276c3+6335a2d+
------------------------------------------------------------------------
1401abd+12128b2d+12282acd-10379bcd-14198c2d-3578ad2-2991bd2-2681cd2+
------------------------------------------------------------------------
13610d3-8644a2e+3650abe+1078b2e+3151ace+15194bce+14356c2e-4824ade-
------------------------------------------------------------------------
1221bde+5805cde+869d2e-6364ae2+12085be2-4380ce2+10091de2+11293e3
------------------------------------------------------------------------
a2b-12263b3+5425a2c-3446abc+14471b2c+3461ac2-13067bc2+7756c3+13141a2d+
------------------------------------------------------------------------
10853abd+14934b2d-4565acd-11104bcd+604c2d-14937ad2-7942bd2+2593cd2-931d3
------------------------------------------------------------------------
+6339a2e+14616abe-7189b2e+10290ace-14895bce-13748c2e-9795ade+1972bde+
------------------------------------------------------------------------
14762cde-10272d2e+3284ae2-9163be2-7275ce2+246de2-4579e3
------------------------------------------------------------------------
a3-11962b3-12223a2c+13348abc+14320b2c+14261ac2+13511bc2-14523c3-12982a2d
------------------------------------------------------------------------
+2633abd+562b2d-15499acd+4594bcd-3822c2d+7351ad2+8674bd2-6178cd2-4311d3+
------------------------------------------------------------------------
14430a2e-14361abe-2583b2e+8317ace-14069bce-6057c2e+7782ade-5354bde+
------------------------------------------------------------------------
491cde-8015d2e+307ae2-7472be2+1954ce2+15722de2-3193e3
------------------------------------------------------------------------
b3c-7332a2c2+8115abc2+14992b2c2-8101ac3-4023bc3+2483c4+3144b3d+7542a2cd+
------------------------------------------------------------------------
14648abcd+13196b2cd+15812ac2d+5661bc2d+3347c3d+2307a2d2-14443abd2+
------------------------------------------------------------------------
8113b2d2-9234acd2-226bcd2+13587c2d2-4322ad3-10906bd3-9086cd3-7471d4-
------------------------------------------------------------------------
14982b3e+10511a2ce-12003abce-14846b2ce+14902ac2e+6652bc2e+14852c3e+
------------------------------------------------------------------------
2585a2de+8948abde-15069b2de+11166acde-8169bcde+3648c2de-740ad2e-3080bd2e
------------------------------------------------------------------------
-12817cd2e-5751d3e-7186a2e2+10779abe2-678b2e2-11436ace2-13149bce2-
------------------------------------------------------------------------
456c2e2-1440ade2+921bde2+11416cde2+13839d2e2+13663ae3-3722be3-11638ce3+
------------------------------------------------------------------------
8766de3+9926e4 b4-1449a2c2-6419abc2-12308b2c2+14458ac3+170bc3-10939c4+
------------------------------------------------------------------------
3258b3d+9732a2cd+9216abcd-4999b2cd-12678ac2d-1921bc2d+14956c3d-4673a2d2-
------------------------------------------------------------------------
5714abd2-885b2d2-9212acd2-2729bcd2-12367c2d2-6487ad3-6044bd3-4862cd3+
------------------------------------------------------------------------
13163d4+2157b3e-6455a2ce-7930abce-7875b2ce-10660ac2e+10601bc2e+3492c3e-
------------------------------------------------------------------------
9346a2de-12833abde-10798b2de+1476acde-948bcde+5950c2de-4939ad2e-2742bd2e
------------------------------------------------------------------------
-5750cd2e-3631d3e-8395a2e2-15849abe2-7749b2e2+11327ace2-7099bce2+
------------------------------------------------------------------------
10852c2e2-4216ade2+9725bde2+917cde2+14334d2e2-9423ae3-12416be3-6758ce3-
------------------------------------------------------------------------
9734de3+8784e4 abc3-13370b2c3+1245ac4+12381bc4+3825c5+14927a2c2d+
------------------------------------------------------------------------
11695abc2d+4863b2c2d-13413ac3d+6323bc3d+2207c4d-10869b3d2+12653a2cd2-
------------------------------------------------------------------------
13503abcd2+15203b2cd2-15370ac2d2-8080bc2d2-696c3d2-3524a2d3-15615abd3+
------------------------------------------------------------------------
11731b2d3+2500acd3-9387bcd3-15120c2d3+9219ad4-10733bd4-14333cd4-3484d5-
------------------------------------------------------------------------
2786a2c2e-10970abc2e-5563b2c2e-12795ac3e+13260bc3e+6389c4e+1419b3de-
------------------------------------------------------------------------
15701a2cde-10638abcde+11714b2cde-552ac2de+12736bc2de-41c3de+7388a2d2e+
------------------------------------------------------------------------
11699abd2e-10072b2d2e-5718acd2e-1683bcd2e+11296c2d2e-4327ad3e+90bd3e-
------------------------------------------------------------------------
3720cd3e-4193d4e+9932b3e2-2614a2ce2-728abce2+446b2ce2+2212ac2e2-
------------------------------------------------------------------------
6903bc2e2+2572c3e2+12595a2de2-7340abde2-10623b2de2-7874acde2+5143bcde2-
------------------------------------------------------------------------
12126c2de2-5509ad2e2+1576bd2e2+2800cd2e2+5905d3e2+13048a2e3+4878abe3+
------------------------------------------------------------------------
14252b2e3+8865ace3-12385bce3-7899c2e3+1828ade3+3034bde3+10271cde3+
------------------------------------------------------------------------
265d2e3-5188ae4+9573be4-4526ce4+10961de4+14273e5
------------------------------------------------------------------------
a2c3-10892b2c3+13826ac4-5313bc4-2836c5+8008a2c2d+4478abc2d+4247b2c2d-
------------------------------------------------------------------------
1121ac3d+3521bc3d+14951c4d-6275b3d2+13906a2cd2+7896abcd2-1000b2cd2+
------------------------------------------------------------------------
1663ac2d2-5656bc2d2+8658c3d2+7397a2d3+15991abd3-2976b2d3-13609acd3+
------------------------------------------------------------------------
11658bcd3-7786c2d3-12858ad4-8518bd4-6459cd4-6723d5-1166a2c2e-7578abc2e+
------------------------------------------------------------------------
4483b2c2e+13549ac3e+11283bc3e-9692c4e+1361b3de-11254a2cde+9576abcde-
------------------------------------------------------------------------
5322b2cde+13447ac2de+9bc2de+5882c3de+1051a2d2e+2218abd2e-2049b2d2e-
------------------------------------------------------------------------
11344acd2e-4801bcd2e+4979c2d2e-11668ad3e+7631bd3e-5256cd3e-10348d4e+
------------------------------------------------------------------------
10948b3e2+3867a2ce2+5973abce2+4878b2ce2-13234ac2e2+460bc2e2+9401c3e2+
------------------------------------------------------------------------
6664a2de2+13833abde2-13027b2de2+3514acde2-11226bcde2+11060c2de2-
------------------------------------------------------------------------
3171ad2e2+5399bd2e2+5008cd2e2+11134d3e2-13762a2e3+9082abe3-3613b2e3+
------------------------------------------------------------------------
8528ace3-7982bce3+13915c2e3-11612ade3-3941bde3+14914cde3+9118d2e3+
------------------------------------------------------------------------
10742ae4+12034be4+12188ce4-4387de4+8666e5 |
1 7
o6 : Matrix R <--- R
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i7 : leadTerm gbSnapshot(I)
o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |
1 7
o7 : Matrix R <--- R
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