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 (4340a + 3655a b + 8191a*b - 3402b - 11778a c - 3192a*b*c +
------------------------------------------------------------------------
2 2 2 3 2 2
1477b c + 11256a*c + 4057b*c - 5028c - 2030a d - 7882a*b*d - 15254b d
------------------------------------------------------------------------
2 2 2 2
+ 6768a*c*d + 8735b*c*d - 1759c d + 12440a*d + 13688b*d - 6988c*d -
------------------------------------------------------------------------
3 2 2
2558d - 4466a e - 8004a*b*e + 5930b e + 12087a*c*e - 10238b*c*e -
------------------------------------------------------------------------
2 2 2
12845c e - 10411a*d*e - 13622b*d*e - 14439c*d*e + 11049d e - 377a*e -
------------------------------------------------------------------------
2 2 2 3 3 2
8329b*e + 14046c*e + 13791d*e + 11467e , - 13818a - 7638a b +
------------------------------------------------------------------------
2 3 2 2 2 2
320a*b - 9384b - 13175a c - 6310a*b*c - 14863b c + 7048a*c - 7571b*c
------------------------------------------------------------------------
3 2 2
- 11289c - 9612a d + 4705a*b*d - 3482b d - 12161a*c*d - 6246b*c*d +
------------------------------------------------------------------------
2 2 2 2 3 2
13453c d - 1643a*d - 6135b*d + 3233c*d + 14378d + 10234a e +
------------------------------------------------------------------------
2 2
7518a*b*e - 8956b e - 4088a*c*e - 27b*c*e - 28c e - 13123a*d*e +
------------------------------------------------------------------------
2 2 2 2
10356b*d*e + 11675c*d*e - 10004d e + 9714a*e - 546b*e - 14349c*e -
------------------------------------------------------------------------
2 3 3 2 2 3 2
9894d*e - 3507e , 15684a + 4555a b + 5445a*b + 273b + 1823a c +
------------------------------------------------------------------------
2 2 2 3 2
10035a*b*c + 12057b c - 9725a*c + 2445b*c - 1321c + 398a d -
------------------------------------------------------------------------
2 2 2
2197a*b*d - 829b d + 4071a*c*d - 2753b*c*d - 10709c d - 437a*d -
------------------------------------------------------------------------
2 2 3 2 2
13089b*d - 7616c*d - 14549d + 1165a e + 3958a*b*e + 13749b e -
------------------------------------------------------------------------
2
8764a*c*e - 702b*c*e - 6812c e - 5300a*d*e + 10496b*d*e + 3852c*d*e +
------------------------------------------------------------------------
2 2 2 2 2 3
6448d e + 10281a*e + 1118b*e - 13952c*e + 3962d*e + 7767e )
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 = | ab2-12858b3-14640a2c-3206abc+7150b2c+10494ac2-144bc2-15225c3-10965a2d+
------------------------------------------------------------------------
6089abd-13376b2d-7536acd+10759bcd-10059c2d+8431ad2-4197bd2-8165cd2+
------------------------------------------------------------------------
11180d3-9821a2e+7144abe+15750b2e-7730ace-11188bce-1390c2e+1166ade-
------------------------------------------------------------------------
8564bde+9101cde-8964d2e+1223ae2+12947be2+6029ce2+2343de2+1213e3
------------------------------------------------------------------------
a2b-8110b3-14353a2c-3986abc+2181b2c-13914ac2-9907bc2-13166c3-5015a2d-
------------------------------------------------------------------------
10666abd-6098b2d+11605acd-387bcd+4264c2d+8449ad2-9065bd2-280cd2+14258d3-
------------------------------------------------------------------------
11272a2e+4617abe+10369b2e-2062ace-11504bce+4925c2e-6211ade-7716bde+
------------------------------------------------------------------------
7922cde+336d2e-10144ae2-7021be2-7572ce2+5379de2+12841e3
------------------------------------------------------------------------
a3+406b3-4816a2c+8758abc+10891b2c+12385ac2-3492bc2+9448c3-15713a2d-
------------------------------------------------------------------------
4893abd+15452b2d+4429acd-46bcd+8093c2d+808ad2-443bd2+11006cd2+5944d3+
------------------------------------------------------------------------
15086a2e-12499abe-3467b2e+9183ace+13620bce+2086c2e+4237ade+138bde-
------------------------------------------------------------------------
9841cde+5643d2e-5195ae2-14417be2+5996ce2-15814de2+14898e3
------------------------------------------------------------------------
b3c+621a2c2-37abc2-7107b2c2-2627ac3+8110bc3-6109c4-6275b3d+11085a2cd+
------------------------------------------------------------------------
6781abcd-750b2cd+13467ac2d-12766bc2d+15894c3d-8821a2d2+7585abd2-
------------------------------------------------------------------------
15127b2d2-11835acd2-3245bcd2+3592c2d2-12038ad3-15937bd3+10879cd3-15046d4
------------------------------------------------------------------------
-10345b3e-15116a2ce+14395abce-10088b2ce+8957ac2e+14938bc2e+1052c3e-
------------------------------------------------------------------------
6246a2de-1382abde+3344b2de-10474acde+10178bcde-2865c2de-7427ad2e+
------------------------------------------------------------------------
1329bd2e-8514cd2e+2945d3e+5832a2e2-14654abe2+5024b2e2-5413ace2+13731bce2
------------------------------------------------------------------------
-8500c2e2+10446ade2-12298bde2+8212cde2+14004d2e2-14758ae3+1722be3-
------------------------------------------------------------------------
8685ce3+14040de3-3104e4
------------------------------------------------------------------------
b4+11415a2c2-13462abc2+6816b2c2-5589ac3+12936bc3+3619c4+13482b3d-
------------------------------------------------------------------------
7719a2cd-4579abcd-15872b2cd-10778ac2d-4362bc2d+7999c3d-3716a2d2+1982abd2
------------------------------------------------------------------------
-13686b2d2+10416acd2+2310bcd2-2515c2d2-14723ad3-4435bd3+8727cd3+1349d4+
------------------------------------------------------------------------
9983b3e+1895a2ce+8499abce+8443b2ce-5235ac2e+2090bc2e+15037c3e+12810a2de-
------------------------------------------------------------------------
3526abde-10081b2de-3118acde+2702bcde+13768c2de-2835ad2e-3062bd2e-
------------------------------------------------------------------------
2851cd2e-16000d3e+14856a2e2-2220abe2+9311b2e2-8596ace2-12920bce2+
------------------------------------------------------------------------
9516c2e2+15311ade2+1235bde2+13736cde2+10630d2e2-2196ae3-15950be3+
------------------------------------------------------------------------
11338ce3-13959de3+14484e4
------------------------------------------------------------------------
abc3+4108b2c3+7996ac4-1535bc4+15890c5-4273a2c2d+1434abc2d+13926b2c2d-
------------------------------------------------------------------------
5532ac3d-14165bc3d-14250c4d+8016b3d2+5596a2cd2+12765abcd2-1530b2cd2+
------------------------------------------------------------------------
11493ac2d2-793bc2d2-9759c3d2-10016a2d3-3432abd3+15960b2d3-13764acd3-
------------------------------------------------------------------------
1198bcd3-1684c2d3-6275ad4-53bd4-15747cd4-3775d5+2979a2c2e+3569abc2e+
------------------------------------------------------------------------
5512b2c2e-15551ac3e-6354bc3e+2769c4e-8275b3de-5264a2cde-3151abcde+
------------------------------------------------------------------------
9476b2cde-2188ac2de-3367bc2de+15266c3de+10927a2d2e-5354abd2e+12899b2d2e+
------------------------------------------------------------------------
14116acd2e-6532bcd2e-4137c2d2e-8962ad3e-10399bd3e-3747cd3e+11181d4e+
------------------------------------------------------------------------
14493b3e2+6930a2ce2-11779abce2+1956b2ce2+13508ac2e2-10701bc2e2+8847c3e2+
------------------------------------------------------------------------
412a2de2-9998abde2-10459b2de2+5005acde2-13947bcde2+5969c2de2+3974ad2e2+
------------------------------------------------------------------------
9855bd2e2-3896cd2e2-14102d3e2+135a2e3+5441abe3-4164b2e3-8219ace3+
------------------------------------------------------------------------
9496bce3-14473c2e3+14218ade3-2142bde3+1064cde3-14503d2e3-10858ae4+
------------------------------------------------------------------------
9588be4-37ce4-3967de4-15208e5
------------------------------------------------------------------------
a2c3+11077b2c3-13596ac4-6981bc4-13948c5+2058a2c2d-11817abc2d+11522b2c2d+
------------------------------------------------------------------------
6265ac3d+806bc3d+5818c4d-1090b3d2-8059a2cd2-4664abcd2-7282b2cd2+
------------------------------------------------------------------------
6921ac2d2+4255bc2d2+10691c3d2+5418a2d3-15577abd3-626b2d3+8631acd3+
------------------------------------------------------------------------
5071bcd3+8879c2d3-11527ad4-4437bd4-7336cd4-643d5-583a2c2e-6506abc2e+
------------------------------------------------------------------------
15788b2c2e+9348ac3e+2992bc3e+5660c4e-14687b3de-1211a2cde-3824abcde-
------------------------------------------------------------------------
13991b2cde-15413ac2de+914bc2de+2604c3de-5820a2d2e+6692abd2e-12473b2d2e+
------------------------------------------------------------------------
12986acd2e+6071bcd2e-1033c2d2e-10353ad3e+5896bd3e-1616cd3e-5427d4e-
------------------------------------------------------------------------
13879b3e2-7889a2ce2-9142abce2-34b2ce2-9325ac2e2-12346bc2e2+2031c3e2+
------------------------------------------------------------------------
10391a2de2+329abde2-7726b2de2-129acde2+1288bcde2-4548c2de2+761ad2e2+
------------------------------------------------------------------------
6307bd2e2-12815cd2e2-12389d3e2+8102a2e3-12186abe3-937b2e3-3330ace3-
------------------------------------------------------------------------
5421bce3+8516c2e3-6726ade3+496bde3-4901cde3+14394d2e3-10134ae4-15639be4+
------------------------------------------------------------------------
243ce4+2457de4+5714e5 |
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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