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 (- 11921a - 4055a b - 321a*b - 13146b - 5657a c + 6751a*b*c -
------------------------------------------------------------------------
2 2 2 3 2
4786b c + 3181a*c + 10367b*c - 13952c - 4285a d - 13345a*b*d -
------------------------------------------------------------------------
2 2 2 2
8173b d + 11514a*c*d + 13676b*c*d - 13145c d + 9022a*d - 15829b*d -
------------------------------------------------------------------------
2 3 2 2
4065c*d - 7251d + 2931a e + 438a*b*e - 2348b e + 11893a*c*e - 954b*c*e
------------------------------------------------------------------------
2 2 2
+ 2537c e + 4424a*d*e + 5494b*d*e - 3496c*d*e + 1825d e - 9680a*e +
------------------------------------------------------------------------
2 2 2 3 3 2 2
3784b*e + 14058c*e - 2181d*e + 8078e , 8711a - 13143a b - 6537a*b +
------------------------------------------------------------------------
3 2 2 2 2 3
11785b - 9307a c - 6918a*b*c - 2245b c + 7237a*c - 202b*c - 156c -
------------------------------------------------------------------------
2 2 2
4941a d - 8122a*b*d + 13513b d + 2958a*c*d - 1710b*c*d - 2875c d -
------------------------------------------------------------------------
2 2 2 3 2
12044a*d - 743b*d - 7753c*d + 9404d - 14676a e - 15833a*b*e +
------------------------------------------------------------------------
2 2
5301b e - 15908a*c*e - 8726b*c*e - 14195c e + 15410a*d*e - 15452b*d*e -
------------------------------------------------------------------------
2 2 2 2 2
14612c*d*e + 8337d e - 10274a*e - 14388b*e + 4671c*e - 510d*e -
------------------------------------------------------------------------
3 3 2 2 3 2
6308e , 10672a + 11602a b - 11454a*b + 10322b - 1173a c - 15745a*b*c
------------------------------------------------------------------------
2 2 2 3 2
- 13874b c - 6571a*c - 15312b*c - 2580c + 9216a d + 10618a*b*d +
------------------------------------------------------------------------
2 2 2 2
5284b d - 15180a*c*d + 7449b*c*d - 14466c d + 531a*d - 5552b*d -
------------------------------------------------------------------------
2 3 2 2
8527c*d - 8697d - 13270a e - 10836a*b*e + 7221b e - 38a*c*e - 561b*c*e
------------------------------------------------------------------------
2 2 2
- 7828c e - 8113a*d*e - 9594b*d*e + 2657c*d*e - 10538d e + 14527a*e -
------------------------------------------------------------------------
2 2 2 3
11632b*e - 3191c*e + 4528d*e + 8304e )
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 = | ab2-15097b3+15813a2c-12753abc+6227b2c+6768ac2+8106bc2-12489c3+11229a2d
------------------------------------------------------------------------
+857abd+7889b2d-10558acd+1740bcd-6847c2d-5152ad2+12394bd2+4738cd2-
------------------------------------------------------------------------
15087d3-1935a2e-1139abe-1561b2e+7197ace+1076bce-5919c2e-6145ade+12123bde
------------------------------------------------------------------------
-9767cde+825d2e-14487ae2-9908be2-12877ce2+855de2+10512e3
------------------------------------------------------------------------
a2b+7866b3-6861a2c+4712abc-14099b2c-12378ac2+13504bc2-6119c3-2378a2d+
------------------------------------------------------------------------
2567abd-13934b2d-6528acd-8464bcd-13053c2d+15675ad2+7412bd2-7971cd2-
------------------------------------------------------------------------
12578d3-11039a2e+9860abe+3182b2e-6423ace+2877bce+895c2e+5826ade-6573bde+
------------------------------------------------------------------------
9835cde+8235d2e+12056ae2-7959be2-3545ce2+3009de2-6917e3
------------------------------------------------------------------------
a3+10320b3-6352a2c+14214abc-8440b2c-13787ac2-9065bc2+12572c3-10210a2d+
------------------------------------------------------------------------
823abd-8801b2d+2673acd+5615bcd+12784c2d+943ad2-2757bd2-13314cd2-5551d3-
------------------------------------------------------------------------
2510a2e+1066abe-10055b2e-2308ace-1778bce-10889c2e+9864ade+10854bde+
------------------------------------------------------------------------
12067cde+6296d2e-8451ae2-3284be2+4934ce2+7147de2-6237e3
------------------------------------------------------------------------
b3c+2080a2c2-3650abc2+1538b2c2-7321ac3+8869bc3+5997c4-2605b3d-9059a2cd+
------------------------------------------------------------------------
1080abcd+15357b2cd-2788ac2d-5168bc2d+4407c3d-11330a2d2+12952abd2-
------------------------------------------------------------------------
2249b2d2+14056acd2-13254bcd2-9794c2d2+8276ad3-1905bd3+8921cd3-8465d4-
------------------------------------------------------------------------
3531b3e+8416a2ce+13309abce-7858b2ce+10640ac2e+14857bc2e+9329c3e+5667a2de
------------------------------------------------------------------------
-15735abde-6884b2de+1740acde-6494bcde+8785c2de+6564ad2e-3335bd2e-
------------------------------------------------------------------------
15675cd2e-2347d3e+5462a2e2-1032abe2-15574b2e2-4090ace2+6215bce2+
------------------------------------------------------------------------
11053c2e2+6906ade2+12845bde2+10883cde2-15291d2e2+2957ae3-1448be3+3869ce3
------------------------------------------------------------------------
+15974de3-14439e4 b4+13264a2c2-15352abc2+7776b2c2-9842ac3-4041bc3-
------------------------------------------------------------------------
10820c4+1801b3d-14204a2cd-1553abcd+3493b2cd+7598ac2d+10401bc2d+4857c3d-
------------------------------------------------------------------------
5306a2d2-58abd2-13641b2d2-9060acd2+8844bcd2+6152c2d2+2413ad3+12808bd3+
------------------------------------------------------------------------
12153cd3-12343d4-10008b3e-10245a2ce-12886abce+12077b2ce+9041ac2e-
------------------------------------------------------------------------
13009bc2e-306c3e-5620a2de+12016abde+2036b2de+15031acde-9469bcde-
------------------------------------------------------------------------
14161c2de-2050ad2e-3177bd2e-14848cd2e+14358d3e+10743a2e2-12194abe2-
------------------------------------------------------------------------
6231b2e2-8473ace2-14169bce2-7690c2e2+11398ade2-13316bde2+502cde2-
------------------------------------------------------------------------
8089d2e2-1428ae3-5399be3-15939ce3+222de3+6243e4
------------------------------------------------------------------------
abc3+15561b2c3+14587ac4+3006bc4-5934c5-12580a2c2d+1930abc2d+6998b2c2d-
------------------------------------------------------------------------
12729ac3d-2172bc3d+7017c4d-11522b3d2-5229a2cd2+14373abcd2+5273b2cd2+
------------------------------------------------------------------------
5961ac2d2+5625bc2d2-4001c3d2-13647a2d3-4965abd3+7005b2d3+1375acd3+
------------------------------------------------------------------------
12166bcd3-1248c2d3+14638ad4-14614bd4-4261cd4+10929d5-7094a2c2e-3866abc2e
------------------------------------------------------------------------
+1893b2c2e-459ac3e-15586bc3e+3226c4e+10463b3de+12858a2cde-11760abcde-
------------------------------------------------------------------------
60b2cde+4761ac2de-15519bc2de+13384c3de+6229a2d2e+10370abd2e-5521b2d2e-
------------------------------------------------------------------------
4951acd2e+4213bcd2e+263c2d2e-15941ad3e+2399bd3e+6147cd3e+2033d4e+
------------------------------------------------------------------------
5436b3e2+46a2ce2+8263abce2+15777b2ce2-392ac2e2+1942bc2e2+4599c3e2-
------------------------------------------------------------------------
6341a2de2+10939abde2-1958b2de2+15805acde2+12209bcde2-14711c2de2+430ad2e2
------------------------------------------------------------------------
-7779bd2e2-8603cd2e2-7067d3e2-13317a2e3+2080abe3+6225b2e3-5774ace3+
------------------------------------------------------------------------
6682bce3+11762c2e3+8854ade3+6421bde3-3218cde3-1549d2e3+4437ae4+9549be4-
------------------------------------------------------------------------
14434ce4+2132de4-15171e5
------------------------------------------------------------------------
a2c3-706b2c3+12627ac4+2878bc4+9400c5-5709a2c2d-756abc2d-5402b2c2d-
------------------------------------------------------------------------
5196ac3d-10888bc3d+8820c4d+4696b3d2-1268a2cd2-1186abcd2+13650b2cd2-
------------------------------------------------------------------------
702ac2d2+15389bc2d2-1418c3d2+3024a2d3+2114abd3-7260b2d3-11964acd3-
------------------------------------------------------------------------
212bcd3-13294c2d3-12348ad4-7478bd4-7863cd4-13855d5+15840a2c2e-1713abc2e-
------------------------------------------------------------------------
2752b2c2e-4357ac3e+6329bc3e-10117c4e-4724b3de-2650a2cde+1081abcde+
------------------------------------------------------------------------
244b2cde-5333ac2de-5713bc2de+740c3de+6849a2d2e-15191abd2e-14189b2d2e+
------------------------------------------------------------------------
15308acd2e+10581bcd2e+2987c2d2e-9329ad3e-5730bd3e+1620cd3e-8598d4e+
------------------------------------------------------------------------
2203b3e2-14035a2ce2-14630abce2+11277b2ce2+15006ac2e2-7123bc2e2-8886c3e2-
------------------------------------------------------------------------
10241a2de2+462abde2+6698b2de2-13394acde2+10873bcde2+5242c2de2-8671ad2e2+
------------------------------------------------------------------------
3827bd2e2+13852cd2e2+5645d3e2-6240a2e3+10379abe3+6649b2e3-5209ace3+
------------------------------------------------------------------------
14846bce3-9604c2e3-1432ade3+13205bde3+2701cde3-7379d2e3+13844ae4-4092be4
------------------------------------------------------------------------
-10096ce4+14020de4-11325e5 |
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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