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 (- 11835a - 9064a b - 11872a*b + 4194b + 6517a c - 4120a*b*c +
------------------------------------------------------------------------
2 2 2 3 2
4176b c + 3072a*c + 7153b*c + 11992c + 12207a d + 12559a*b*d -
------------------------------------------------------------------------
2 2 2 2
8543b d - 5028a*c*d - 7153b*c*d + 11009c d + 8935a*d - 12006b*d -
------------------------------------------------------------------------
2 3 2 2
2720c*d - 9705d - 15043a e - 13243a*b*e - 8037b e - 14955a*c*e -
------------------------------------------------------------------------
2 2
12850b*c*e + 5364c e + 8217a*d*e - 9624b*d*e - 14121c*d*e - 4521d e -
------------------------------------------------------------------------
2 2 2 2 3 3 2
2837a*e + 3573b*e + 4318c*e + 8773d*e + 5999e , 10426a - 13385a b +
------------------------------------------------------------------------
2 3 2 2 2
12395a*b + 5554b + 14215a c + 15374a*b*c + 11492b c - 13664a*c +
------------------------------------------------------------------------
2 3 2 2
8301b*c + 5596c - 2457a d + 28a*b*d - 14178b d - 15924a*c*d +
------------------------------------------------------------------------
2 2 2 2 3 2
6300b*c*d - 3711c d + 6635a*d - 2795b*d + 3573c*d - 15223d + 7271a e
------------------------------------------------------------------------
2 2
- 14108a*b*e + 9774b e - 1012a*c*e - 4065b*c*e + 4519c e + 3927a*d*e +
------------------------------------------------------------------------
2 2 2 2
3989b*d*e + 4955c*d*e - 7981d e + 8514a*e - 11208b*e - 10099c*e -
------------------------------------------------------------------------
2 3 3 2 2 3 2
2475d*e - 14237e , 3065a + 864a b + 14186a*b + 9037b + 13827a c +
------------------------------------------------------------------------
2 2 2 3 2
4178a*b*c + 15727b c + 11925a*c + 62b*c - 1858c - 14794a d +
------------------------------------------------------------------------
2 2 2
14438a*b*d + 3617b d + 4329a*c*d + 13196b*c*d + 4621c d - 3112a*d -
------------------------------------------------------------------------
2 2 3 2 2
2921b*d - 5097c*d + 2361d + 12697a e - 2601a*b*e + 462b e -
------------------------------------------------------------------------
2
11609a*c*e + 2022b*c*e + 4560c e + 9362a*d*e + 13642b*d*e - 12835c*d*e -
------------------------------------------------------------------------
2 2 2 2 2 3
13621d e - 4427a*e + 13948b*e + 8967c*e + 1318d*e - 788e )
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+10125b3+10839a2c+6583abc-9405b2c-434ac2+12970bc2-14170c3-12778a2d-
------------------------------------------------------------------------
7925abd+6609b2d+12907acd-2509bcd+12743c2d+3556ad2-13556bd2+15705cd2-
------------------------------------------------------------------------
12167d3+10510a2e-8663abe+14440b2e-3805ace-7524bce+5497c2e+7100ade-
------------------------------------------------------------------------
7651bde+6346cde-6879d2e-5506ae2+14648be2+10948ce2-1920de2+6946e3
------------------------------------------------------------------------
a2b+2173b3+7670a2c-10198abc-5486b2c+15782ac2-14692bc2+9235c3+11841a2d+
------------------------------------------------------------------------
7358abd-1640b2d-10278acd-10828bcd+14647c2d-9902ad2-11756bd2+2720cd2+
------------------------------------------------------------------------
14634d3+7790a2e-4835abe+5850b2e+5325ace+592bce+1470c2e+14689ade+3095bde+
------------------------------------------------------------------------
12000cde+8341d2e+7437ae2+12334be2-13432ce2+983de2+10610e3
------------------------------------------------------------------------
a3-2365b3-6445a2c+6718abc+3817b2c+15711ac2-13914bc2+15169c3-13950a2d-
------------------------------------------------------------------------
9160abd-13012b2d+9954acd+897bcd-8707c2d+14367ad2+1757bd2-6277cd2+5944d3-
------------------------------------------------------------------------
759a2e-9747abe-14960b2e-6155ace+3323bce-10099c2e+15918ade+5976bde-
------------------------------------------------------------------------
9871cde+8882d2e-6654ae2+7376be2-4584ce2-7021de2-12033e3
------------------------------------------------------------------------
b3c+3005a2c2-8393abc2-10334b2c2+9431ac3+5874bc3+5976c4+6202b3d-11591a2cd
------------------------------------------------------------------------
+5016abcd+6116b2cd+13291ac2d+9132bc2d+10538c3d+2135a2d2-5402abd2+
------------------------------------------------------------------------
4666b2d2-5291acd2+3778bcd2+6543c2d2+201ad3-5329bd3-12273cd3-1463d4+
------------------------------------------------------------------------
12079b3e-13199a2ce-9358abce+2490b2ce+14214ac2e-7138bc2e+9974c3e-6485a2de
------------------------------------------------------------------------
+12148abde+5741b2de+4627acde-9536bcde+31c2de-10357ad2e+4588bd2e-9041cd2e
------------------------------------------------------------------------
-6566d3e-9559a2e2+4816abe2-3074b2e2+8202ace2+352bce2-10928c2e2-6022ade2+
------------------------------------------------------------------------
1780bde2-6612cde2+3229d2e2+1099ae3-11368be3+9770ce3+15076de3-5899e4
------------------------------------------------------------------------
b4-8476a2c2+4457abc2+1182b2c2+11441ac3+4789bc3+4421c4-14378b3d+7010a2cd+
------------------------------------------------------------------------
4384abcd+8953b2cd+5419ac2d-8050bc2d+2824c3d+6405a2d2-7699abd2+12847b2d2-
------------------------------------------------------------------------
12878acd2+12166bcd2+3344c2d2+901ad3-15043bd3-2971cd3-3707d4-6330b3e-
------------------------------------------------------------------------
6174a2ce+12814abce-3426b2ce+7972ac2e+6808bc2e+12092c3e-10572a2de+
------------------------------------------------------------------------
3121abde+2989b2de+969acde-1562bcde-11415c2de-3058ad2e+3818bd2e-4102cd2e+
------------------------------------------------------------------------
12387d3e+11527a2e2+6244abe2-14115b2e2+13763ace2-13343bce2-9829c2e2+
------------------------------------------------------------------------
8676ade2-2241bde2-12764cde2-361d2e2+576ae3+7653be3+8224ce3-10102de3-
------------------------------------------------------------------------
13178e4 abc3-10536b2c3-5277ac4+7327bc4+2766c5-17a2c2d-15042abc2d-
------------------------------------------------------------------------
10546b2c2d+12521ac3d+2871bc3d+15695c4d-5875b3d2-6164a2cd2-14766abcd2+
------------------------------------------------------------------------
2397b2cd2-1902ac2d2-4076bc2d2-10841c3d2-5051a2d3+896abd3+5020b2d3-
------------------------------------------------------------------------
8831acd3+4560bcd3-14022c2d3-14713ad4-8349bd4-12990cd4+2529d5+601a2c2e-
------------------------------------------------------------------------
91abc2e+8491b2c2e+12970ac3e-13374bc3e-8053c4e-1682b3de+1701a2cde-
------------------------------------------------------------------------
8283abcde+15229b2cde+1163ac2de-8450bc2de-11667c3de+8893a2d2e-1643abd2e+
------------------------------------------------------------------------
4196b2d2e-5950acd2e-14524bcd2e-6102c2d2e+14655ad3e-10572bd3e-9076cd3e+
------------------------------------------------------------------------
5542d4e+1426b3e2-4220a2ce2-6676abce2+12012b2ce2-6306ac2e2+15726bc2e2+
------------------------------------------------------------------------
28c3e2-7993a2de2-10951abde2+11486b2de2-15777acde2+741bcde2+9742c2de2+
------------------------------------------------------------------------
5006ad2e2+4664bd2e2-14729cd2e2-12024d3e2+9821a2e3-9323abe3-6001b2e3-
------------------------------------------------------------------------
7719ace3-15772bce3+15403c2e3-7354ade3+12245bde3+3833cde3+7829d2e3-
------------------------------------------------------------------------
13832ae4+13210be4-8676ce4+13766de4+5840e5
------------------------------------------------------------------------
a2c3+2914b2c3-6058ac4-11726bc4+5384c5-11989a2c2d+11629abc2d-14823b2c2d+
------------------------------------------------------------------------
6903ac3d+8297bc3d-11540c4d+13729b3d2-3816a2cd2-6341abcd2+1947b2cd2-
------------------------------------------------------------------------
3729ac2d2+3158bc2d2+469c3d2-8587a2d3+13692abd3+1229b2d3-13608acd3+
------------------------------------------------------------------------
14460bcd3+14014c2d3-8522ad4-2987bd4+15009cd4+3748d5-11242a2c2e+4444abc2e
------------------------------------------------------------------------
+13451b2c2e-9063ac3e+14666bc3e+15017c4e-12575b3de-14002a2cde+15795abcde-
------------------------------------------------------------------------
9262b2cde+6790ac2de-14377bc2de+7768c3de-6760a2d2e-4723abd2e-14530b2d2e+
------------------------------------------------------------------------
9306acd2e+3199bcd2e+11310c2d2e-13043ad3e+14489bd3e-6091cd3e-5541d4e+
------------------------------------------------------------------------
8090b3e2+8586a2ce2-13684abce2-13841b2ce2-8575ac2e2+1248bc2e2+14967c3e2+
------------------------------------------------------------------------
12841a2de2+12610abde2-15247b2de2-5426acde2+5338bcde2+6848c2de2+501ad2e2+
------------------------------------------------------------------------
7458bd2e2+3787cd2e2-812d3e2+5100a2e3-142abe3-12764b2e3-3706ace3+
------------------------------------------------------------------------
14372bce3+3594c2e3-4865ade3+6422bde3+10448cde3+11086d2e3-12256ae4+
------------------------------------------------------------------------
5876be4+4734ce4-15302de4-9089e5 |
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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