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 (12134a - 13549a b + 9974a*b - 3853b - 14383a c + 12332a*b*c +
------------------------------------------------------------------------
2 2 2 3 2
7921b c - 8383a*c - 12760b*c + 11928c + 3326a d - 10665a*b*d +
------------------------------------------------------------------------
2 2 2 2
14315b d - 10436a*c*d + 1718b*c*d + 15317c d + 11439a*d + 5301b*d -
------------------------------------------------------------------------
2 3 2 2
11588c*d + 3835d + 8732a e - 15470a*b*e - 5285b e + 2607a*c*e +
------------------------------------------------------------------------
2 2
10655b*c*e + 7868c e - 14448a*d*e + 7686b*d*e - 2573c*d*e - 14641d e -
------------------------------------------------------------------------
2 2 2 2 3 3 2
11311a*e - 7341b*e - 9868c*e + 13311d*e + 7844e , 2289a - 13823a b
------------------------------------------------------------------------
2 3 2 2 2
+ 9635a*b - 14588b - 572a c - 4014a*b*c + 3381b c - 3528a*c +
------------------------------------------------------------------------
2 3 2 2
11148b*c - 3803c - 6208a d - 5657a*b*d + 8347b d + 7455a*c*d -
------------------------------------------------------------------------
2 2 2 2 3
9478b*c*d - 11993c d - 1341a*d + 2209b*d + 8411c*d + 15920d -
------------------------------------------------------------------------
2 2 2
10230a e - 8424a*b*e + 11642b e - 852a*c*e - 4157b*c*e + 11627c e -
------------------------------------------------------------------------
2 2 2
9513a*d*e + 3049b*d*e - 3961c*d*e - 5119d e - 4480a*e - 14183b*e +
------------------------------------------------------------------------
2 2 3 3 2 2 3
2488c*e + 9228d*e - 3166e , - 7219a - 15092a b + 4398a*b - 13577b +
------------------------------------------------------------------------
2 2 2 2 3 2
15156a c - 11139a*b*c + 955b c - 7909a*c - 2616b*c + 9958c + 8199a d
------------------------------------------------------------------------
2 2 2
- 10169a*b*d + 14607b d - 4368a*c*d - 15993b*c*d - 3485c d + 88a*d +
------------------------------------------------------------------------
2 2 3 2 2
7075b*d + 1319c*d + 1503d - 1017a e + 15778a*b*e + 1925b e -
------------------------------------------------------------------------
2
8640a*c*e + 12829b*c*e - 13311c e - 493a*d*e + 15404b*d*e - 8c*d*e +
------------------------------------------------------------------------
2 2 2 2 2 3
2330d e - 13758a*e + 15059b*e - 12213c*e - 13311d*e + 3907e )
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+12631b3+11909a2c+388abc-9872b2c-2457ac2+2791bc2+12511c3+458a2d+
------------------------------------------------------------------------
3299abd+15722b2d+599acd-8667bcd+12185c2d+12558ad2+12793bd2+13251cd2+
------------------------------------------------------------------------
2532d3+4867a2e-7941abe+5385b2e-6202ace-11256bce+10697c2e-733ade-3153bde+
------------------------------------------------------------------------
10553cde-14432d2e+6952ae2-13579be2+7843ce2-13958de2+7737e3
------------------------------------------------------------------------
a2b+5252b3+8649a2c-6012abc+12757b2c+9042ac2+11226bc2-4770c3+4329a2d-
------------------------------------------------------------------------
9362abd-4780b2d-9101acd+7953bcd+3798c2d+4904ad2+6017bd2+5770cd2-469d3-
------------------------------------------------------------------------
7389a2e+7696abe-14528b2e-13424ace+11592bce-7788c2e-3436ade-5047bde+
------------------------------------------------------------------------
13697cde-10217d2e+15501ae2+7880be2+2969ce2+13244de2-11287e3
------------------------------------------------------------------------
a3+12517b3-6874a2c-14648abc-15878b2c-1159ac2+4179bc2-12402c3-9455a2d-
------------------------------------------------------------------------
5552abd+3038b2d+8052acd-11686bcd+7796c2d-5993ad2+14365bd2-8206cd2+8747d3
------------------------------------------------------------------------
+14343a2e+3462abe+11172b2e+503ace+3769bce+12737c2e-13474ade-12815bde+
------------------------------------------------------------------------
15587cde+3940d2e+4029ae2-13781be2-2961ce2+9871de2-8663e3
------------------------------------------------------------------------
b3c+6947a2c2+3732abc2-5872b2c2+14448ac3+824bc3+3658c4+7070b3d+11266a2cd+
------------------------------------------------------------------------
4674abcd+8478b2cd-13095ac2d+8752bc2d+4514c3d+5980a2d2+2575abd2+1545b2d2+
------------------------------------------------------------------------
15650acd2-1241bcd2+545c2d2-5193ad3-13083bd3+5000cd3-12590d4-11353b3e-
------------------------------------------------------------------------
14039a2ce+799abce-9791b2ce-11787ac2e+156bc2e+11926c3e+624a2de+13346abde+
------------------------------------------------------------------------
3197b2de-1093acde+9151bcde-2866c2de+7725ad2e-10386bd2e-9709cd2e+3333d3e+
------------------------------------------------------------------------
4414a2e2-5887abe2+13439b2e2+7494ace2-12756bce2+7986c2e2+12247ade2-
------------------------------------------------------------------------
12024bde2-5246cde2+6715d2e2+851ae3+7950be3+2765ce3-4243de3+6012e4
------------------------------------------------------------------------
b4-14853a2c2+10654abc2-3597b2c2+669ac3-15577bc3-1335c4+12782b3d-
------------------------------------------------------------------------
15515a2cd+11713abcd-5233b2cd-13670ac2d+6015bc2d+6409c3d+11498a2d2-
------------------------------------------------------------------------
15099abd2+7475b2d2+8499acd2-9173bcd2-4401c2d2+840ad3-8370bd3+5339cd3-
------------------------------------------------------------------------
14649d4+6935b3e+7499a2ce-13034abce+10841b2ce+8519ac2e+15887bc2e+11566c3e
------------------------------------------------------------------------
+10139a2de+10523abde-5368b2de+12381acde-15313bcde-6090c2de+12094ad2e+
------------------------------------------------------------------------
216bd2e-14304cd2e-821d3e+1112a2e2+11545abe2-5273b2e2-12451ace2-9875bce2-
------------------------------------------------------------------------
12730c2e2-9765ade2-13477bde2-8023cde2-12462d2e2-8701ae3-13696be3-
------------------------------------------------------------------------
14866ce3-112de3-1807e4 abc3+7829b2c3-2486ac4+14749bc4-13147c5-13239a2c2d
------------------------------------------------------------------------
-1336abc2d-12601b2c2d+2726ac3d+15889bc3d-643c4d-4043b3d2+9308a2cd2-
------------------------------------------------------------------------
11699abcd2-5368b2cd2-11486ac2d2+9875bc2d2-784c3d2+6642a2d3-15972abd3+
------------------------------------------------------------------------
8191b2d3+11443acd3+11640bcd3+7802c2d3-13762ad4+29bd4-5452cd4-3245d5+
------------------------------------------------------------------------
5288a2c2e+4676abc2e-12438b2c2e+7954ac3e-4392bc3e-15022c4e-13591b3de-
------------------------------------------------------------------------
13194a2cde+2427abcde-3321b2cde-10517ac2de+4011bc2de+702c3de+1201a2d2e-
------------------------------------------------------------------------
5251abd2e+7838b2d2e-7052acd2e-11659bcd2e+2959c2d2e+15461ad3e+1080bd3e+
------------------------------------------------------------------------
5501cd3e-3541d4e+2095b3e2+2400a2ce2-4097abce2-172b2ce2-13995ac2e2+
------------------------------------------------------------------------
15698bc2e2-8318c3e2-9464a2de2+5684abde2+12070b2de2-2087acde2-6753bcde2+
------------------------------------------------------------------------
15984c2de2-12257ad2e2-12280bd2e2+6331cd2e2-8906d3e2+1152a2e3-3105abe3-
------------------------------------------------------------------------
6305b2e3-13197ace3+13610bce3+14127c2e3-11498ade3+8567bde3+2008cde3-
------------------------------------------------------------------------
3858d2e3+11174ae4+14531be4+3868ce4-4967de4-5970e5
------------------------------------------------------------------------
a2c3+10391b2c3+15852ac4+3843bc4-12273c5-15291a2c2d-10150abc2d-363b2c2d-
------------------------------------------------------------------------
6575ac3d+2802bc3d+10543c4d-14970b3d2-11581a2cd2+10136abcd2-2953b2cd2-
------------------------------------------------------------------------
15574ac2d2+6342bc2d2+10949c3d2-10519a2d3-4609abd3+14658b2d3-12922acd3+
------------------------------------------------------------------------
5056bcd3+6957c2d3-2961ad4-10018bd4-15814cd4-3864d5-12263a2c2e+8561abc2e-
------------------------------------------------------------------------
3107b2c2e-10556ac3e-3813bc3e-15212c4e+7233b3de+8456a2cde+7786abcde+
------------------------------------------------------------------------
9507b2cde-15115ac2de-13571bc2de+15425c3de-13424a2d2e+14332abd2e+
------------------------------------------------------------------------
5179b2d2e+8966acd2e-9137bcd2e-4234c2d2e-14847ad3e-11443bd3e+9503cd3e-
------------------------------------------------------------------------
8195d4e-8464b3e2-12694a2ce2-10087abce2-4292b2ce2+13991ac2e2-8302bc2e2+
------------------------------------------------------------------------
14092c3e2+2287a2de2-15428abde2-8552b2de2-6537acde2+9427bcde2-529c2de2-
------------------------------------------------------------------------
2283ad2e2-10748bd2e2+11730cd2e2-2832d3e2+8866a2e3+10385abe3-3063b2e3+
------------------------------------------------------------------------
9088ace3-6358bce3+7399c2e3+2652ade3+13230bde3+2943cde3+15246d2e3-
------------------------------------------------------------------------
11154ae4+14177be4-3442ce4-5923de4+11568e5 |
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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