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 (2252a + 8187a b - 8921a*b + 2641b - 10811a c + 10159a*b*c -
------------------------------------------------------------------------
2 2 2 3 2 2
8198b c + 2716a*c - 12299b*c - 5442c + 3161a d - 1395a*b*d + 8203b d
------------------------------------------------------------------------
2 2 2 2
- 10442a*c*d - 1558b*c*d - 1420c d + 15136a*d + 14373b*d + 14001c*d -
------------------------------------------------------------------------
3 2 2
14770d + 13366a e + 13459a*b*e + 9140b e - 8411a*c*e - 5560b*c*e -
------------------------------------------------------------------------
2 2 2
3909c e - 13341a*d*e - 13353b*d*e - 4607c*d*e + 9519d e + 2944a*e +
------------------------------------------------------------------------
2 2 2 3 3 2 2
8863b*e + 14142c*e + 6830d*e - 11287e , 7244a - 9250a b + 3644a*b -
------------------------------------------------------------------------
3 2 2 2 2 3
1227b + 12345a c + 7343a*b*c - 7722b c + 8717a*c + 7294b*c + 13232c
------------------------------------------------------------------------
2 2 2
+ 6466a d + 1017a*b*d - 14670b d + 4520a*c*d - 8666b*c*d - 10859c d -
------------------------------------------------------------------------
2 2 2 3 2 2
6381a*d + 5932b*d + 9915c*d + 6848d + 5766a e + 3974a*b*e - 7831b e
------------------------------------------------------------------------
2
+ 14a*c*e + 9051b*c*e - 2348c e + 12097a*d*e + 10890b*d*e - 3888c*d*e +
------------------------------------------------------------------------
2 2 2 2 2 3 3
3912d e - 6369a*e - 7181b*e - 9575c*e + 4938d*e - 12965e , - 9709a
------------------------------------------------------------------------
2 2 3 2 2
- 15674a b - 12176a*b - 9299b + 6911a c + 14015a*b*c - 2392b c +
------------------------------------------------------------------------
2 2 3 2 2
774a*c + 2540b*c - 183c + 9701a d - 12278a*b*d - 13872b d -
------------------------------------------------------------------------
2 2 2 2
11322a*c*d + 2991b*c*d + 1566c d - 2906a*d + 2421b*d - 4883c*d +
------------------------------------------------------------------------
3 2 2
13936d - 4639a e + 4601a*b*e - 3433b e + 534a*c*e + 1897b*c*e -
------------------------------------------------------------------------
2 2 2
12337c e + 11329a*d*e + 10163b*d*e - 10528c*d*e - 1732d e - 6835a*e +
------------------------------------------------------------------------
2 2 2 3
13068b*e - 9355c*e + 4714d*e - 11674e )
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 = | ab2-14505b3+2680a2c-12053abc-2976b2c-12417ac2-12237bc2+6836c3-3058a2d-
------------------------------------------------------------------------
14313abd-2918b2d+435acd+13893bcd-9555c2d+3693ad2+15879bd2-7116cd2-
------------------------------------------------------------------------
12866d3+12610a2e+6676abe-11907b2e+293ace+11310bce-13768c2e-8920ade-43bde
------------------------------------------------------------------------
-11232cde+1518d2e+6460ae2+12114be2+13526ce2+14656de2-7216e3
------------------------------------------------------------------------
a2b-12464b3+11705a2c-1405abc+3381b2c-3903ac2+27bc2+13641c3+8453a2d-
------------------------------------------------------------------------
11804abd-2406b2d+1611acd+2329bcd-14597c2d-10560ad2+5531bd2-5751cd2+
------------------------------------------------------------------------
4887d3-14671a2e-5085abe-10829b2e-2262ace+9694bce+14718c2e+4994ade+
------------------------------------------------------------------------
7487bde+15138cde-4035d2e-13748ae2+4755be2+15681ce2-7242de2+1169e3
------------------------------------------------------------------------
a3-7201b3+5661a2c+8710abc+1254b2c+4281ac2-7893bc2+7770c3+9965a2d-
------------------------------------------------------------------------
11968abd+15367b2d-7094acd-12834bcd-5533c2d+10294ad2-9168bd2-10544cd2-
------------------------------------------------------------------------
8784d3+194a2e+1936abe-14276b2e-3239ace+13083bce-13105c2e+3077ade-9219bde
------------------------------------------------------------------------
+3173cde+6163d2e-2361ae2+10867be2+119ce2-8835de2+12777e3
------------------------------------------------------------------------
b3c-a2c2+10534abc2-14133b2c2-9960ac3-8890bc3+12800c4+9235b3d-14340a2cd-
------------------------------------------------------------------------
9510abcd-13989b2cd-1026ac2d+12152bc2d+7175c3d-15375a2d2-752abd2-3886b2d2
------------------------------------------------------------------------
+3271acd2+1321bcd2-14056c2d2-8759ad3-15354bd3+6444cd3-10465d4-15782b3e-
------------------------------------------------------------------------
8291a2ce+2680abce+11888b2ce+4796ac2e+14810bc2e-10805c3e+3126a2de-
------------------------------------------------------------------------
12284abde-8064b2de+7865acde-1278bcde+15059c2de-6591ad2e+11644bd2e-
------------------------------------------------------------------------
1529cd2e-9590d3e-13566a2e2-14433abe2+8822b2e2-9525ace2+2041bce2+6823c2e2
------------------------------------------------------------------------
+14891ade2-11724bde2-13475cde2-11329d2e2+10999ae3-22be3+6075ce3+11681de3
------------------------------------------------------------------------
+542e4 b4-4001a2c2+5902abc2+10654b2c2+3208ac3-9534bc3+7599c4-4230b3d+
------------------------------------------------------------------------
14811a2cd+13790abcd-3406b2cd-9725ac2d+907bc2d-3231c3d+2849a2d2+9659abd2+
------------------------------------------------------------------------
4762b2d2-12151acd2+14526bcd2+5670c2d2-11079ad3-15553bd3-1673cd3-15970d4+
------------------------------------------------------------------------
3498b3e+2122a2ce+14986abce-15338b2ce+15912ac2e-12242bc2e-504c3e+
------------------------------------------------------------------------
12509a2de+15319abde+13896b2de+11757acde+13136bcde+5170c2de+13826ad2e+
------------------------------------------------------------------------
7443bd2e-9091cd2e-15974d3e+3397a2e2+13797abe2+10760b2e2-14690ace2-
------------------------------------------------------------------------
2264bce2-6705c2e2-4379ade2-11863bde2+5039cde2+13214d2e2+10892ae3+6803be3
------------------------------------------------------------------------
+10983ce3+9862de3+4293e4
------------------------------------------------------------------------
abc3-6706b2c3-754ac4-7637bc4-1075c5-8383a2c2d-13558abc2d+7244b2c2d-
------------------------------------------------------------------------
1449ac3d-7749bc3d+6473c4d+11187b3d2+3274a2cd2-6737abcd2+11242b2cd2-
------------------------------------------------------------------------
13121ac2d2+3414bc2d2-7592c3d2+1669a2d3+15152abd3+10939b2d3-5059acd3-
------------------------------------------------------------------------
4959bcd3-14311c2d3+3879ad4-3831bd4-4546cd4-13541d5-221a2c2e-10425abc2e+
------------------------------------------------------------------------
5673b2c2e-12306ac3e+3510bc3e+6355c4e+10007b3de-2952a2cde+13910abcde+
------------------------------------------------------------------------
1576b2cde-9504ac2de+9067bc2de+8663c3de-4222a2d2e-6514abd2e-4640b2d2e+
------------------------------------------------------------------------
3265acd2e-9823bcd2e+13169c2d2e+6035ad3e+14380bd3e-6668cd3e+12280d4e-
------------------------------------------------------------------------
1129b3e2-1318a2ce2-15719abce2-3933b2ce2-14278ac2e2-8717bc2e2-10254c3e2+
------------------------------------------------------------------------
15224a2de2-7847abde2+5022b2de2-9590acde2-13202bcde2+7290c2de2+4329ad2e2+
------------------------------------------------------------------------
1274bd2e2-9928cd2e2-6310d3e2+13941a2e3+8626abe3-1891b2e3-13282ace3+
------------------------------------------------------------------------
8333bce3-1005c2e3-3636ade3+15140bde3+9847cde3+13505d2e3+14953ae4-
------------------------------------------------------------------------
10928be4-645ce4+5464de4-7512e5
------------------------------------------------------------------------
a2c3+13092b2c3-1603ac4-2028bc4-4500c5-3840a2c2d+14878abc2d-11275b2c2d-
------------------------------------------------------------------------
11101ac3d+3962bc3d-8318c4d-6399b3d2+12229a2cd2+12239abcd2-8542b2cd2+
------------------------------------------------------------------------
15488ac2d2+9093bc2d2+12943c3d2+12344a2d3-3680abd3+9839b2d3-3855acd3-
------------------------------------------------------------------------
14014bcd3-15311c2d3-15568ad4+982bd4-10608cd4+9016d5+2866a2c2e+1766abc2e+
------------------------------------------------------------------------
8301b2c2e-177ac3e-545bc3e-9856c4e-2389b3de+1722a2cde-206abcde+1088b2cde+
------------------------------------------------------------------------
9547ac2de+8514bc2de+13658c3de-14638a2d2e-5952abd2e+4054b2d2e-13452acd2e-
------------------------------------------------------------------------
8938bcd2e-11769c2d2e+1999ad3e+3394bd3e-7775cd3e-10662d4e-3479b3e2-
------------------------------------------------------------------------
4410a2ce2+3335abce2-221b2ce2-5415ac2e2-3959bc2e2-10570c3e2-7493a2de2+
------------------------------------------------------------------------
13743abde2-2522b2de2+1054acde2-9129bcde2+11046c2de2+13647ad2e2-7077bd2e2
------------------------------------------------------------------------
+1135cd2e2+4669d3e2-9688a2e3+12524abe3+14689b2e3+8133ace3-12720bce3-
------------------------------------------------------------------------
261c2e3+7193ade3+5916bde3+8874cde3-13911d2e3-6701ae4+14228be4-8458ce4+
------------------------------------------------------------------------
11103de4-13930e5 |
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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