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 (- 6893a + 5820a b - 1644a*b - 8738b - 6674a c + 4171a*b*c +
------------------------------------------------------------------------
2 2 2 3 2 2
6386b c + 1980a*c - 1108b*c + 9189c + 2833a d - 2299a*b*d - 9200b d +
------------------------------------------------------------------------
2 2 2 2
1753a*c*d + 8100b*c*d - 14876c d - 2101a*d + 8302b*d + 15993c*d +
------------------------------------------------------------------------
3 2 2
5132d + 12957a e - 6757a*b*e + 7746b e - 1302a*c*e + 3777b*c*e +
------------------------------------------------------------------------
2 2 2
11614c e + 9624a*d*e + 7457b*d*e + 13847c*d*e - 3105d e - 13139a*e -
------------------------------------------------------------------------
2 2 2 3 3 2
13323b*e - 2642c*e + 4241d*e - 15650e , - 2891a - 8400a b -
------------------------------------------------------------------------
2 3 2 2 2
13742a*b - 2256b - 5218a c - 5549a*b*c - 2221b c + 6987a*c +
------------------------------------------------------------------------
2 3 2 2
15787b*c + 15908c + 14457a d + 9938a*b*d - 15818b d - 4794a*c*d -
------------------------------------------------------------------------
2 2 2 2 3
12915b*c*d + 11746c d - 14953a*d - 12863b*d + 12454c*d - 8233d +
------------------------------------------------------------------------
2 2 2
8687a e - 14332a*b*e - 4553b e + 3017a*c*e + 8086b*c*e - 1397c e -
------------------------------------------------------------------------
2 2 2
15528a*d*e - 5554b*d*e - 6477c*d*e - 4109d e - 8852a*e - 13580b*e +
------------------------------------------------------------------------
2 2 3 3 2 2 3
12553c*e + 3548d*e + 3242e , 818a + 9127a b + 3780a*b - 7643b +
------------------------------------------------------------------------
2 2 2 2 3 2
9335a c + 5251a*b*c - 7896b c + 6971a*c + 14542b*c - 14131c + 1175a d
------------------------------------------------------------------------
2 2 2
+ 7814a*b*d + 12801b d + 13748a*c*d + 8791b*c*d - 9652c d - 10135a*d -
------------------------------------------------------------------------
2 2 3 2 2
11193b*d + 12762c*d - 11427d - 6116a e - 13039a*b*e - 3801b e +
------------------------------------------------------------------------
2
2127a*c*e + 2470b*c*e + 11881c e + 11981a*d*e - 10403b*d*e - 11908c*d*e
------------------------------------------------------------------------
2 2 2 2 2 3
+ 1508d e - 5959a*e + 3577b*e - 2461c*e - 10728d*e - 15568e )
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 = | ab2-13346b3+622a2c+14295abc-445b2c+3335ac2+10413bc2+14680c3+15914a2d+
------------------------------------------------------------------------
11185abd-9285b2d+4981acd-773bcd+14855c2d-1402ad2+13526bd2-15188cd2+
------------------------------------------------------------------------
7263d3+12007a2e-3840abe+6279b2e+22ace+6419bce+11633c2e+1877ade-10085bde-
------------------------------------------------------------------------
3991cde+2332d2e-8567ae2+608be2-8459ce2+3705de2+7158e3
------------------------------------------------------------------------
a2b+14241b3-4404a2c+7028abc-1113b2c+9442ac2+11627bc2-9929c3-8465a2d-
------------------------------------------------------------------------
4128abd-8864b2d+13827acd+13860bcd+13629c2d-3135ad2+5356bd2+9127cd2-
------------------------------------------------------------------------
7033d3+4647a2e-12573abe+348b2e+9958ace+9718bce+5199c2e-995ade+963bde-
------------------------------------------------------------------------
11247cde-1896d2e+3391ae2-7683be2-11818ce2-5103de2+4364e3
------------------------------------------------------------------------
a3-6311b3-10649a2c-141abc+4254b2c-11873ac2-3693bc2-5191c3-14690a2d-
------------------------------------------------------------------------
9217abd-14944b2d+3355acd-5641bcd+7247c2d-5033ad2+139bd2+14177cd2-15824d3
------------------------------------------------------------------------
-14189a2e+13023abe+9859b2e+14731ace+11753bce+2881c2e-6712ade-3278bde+
------------------------------------------------------------------------
9686cde-5973d2e-3732ae2+10228be2+7138ce2-2254de2+6474e3
------------------------------------------------------------------------
b3c-10577a2c2-15296abc2+13752b2c2-2334ac3+13011bc3-13143c4-4988b3d+
------------------------------------------------------------------------
15101a2cd-4773abcd-11269b2cd+10427ac2d-15330bc2d-3058c3d+3249a2d2-
------------------------------------------------------------------------
9440abd2-7395b2d2-13350acd2+8266bcd2-9136c2d2+5304ad3+1743bd3+14985cd3-
------------------------------------------------------------------------
15665d4-15471b3e+9693a2ce-12069abce-15962b2ce+11662ac2e+13513bc2e+
------------------------------------------------------------------------
13763c3e-8174a2de-5475abde+4005b2de+3720acde+1376bcde-4330c2de+13210ad2e
------------------------------------------------------------------------
+15542bd2e-10932cd2e+13870d3e-3923a2e2-3773abe2+9767b2e2+11080ace2+
------------------------------------------------------------------------
5539bce2+9419c2e2-6840ade2+3184bde2+422cde2-15290d2e2-1293ae3-8471be3+
------------------------------------------------------------------------
5802ce3+10680de3+7303e4
------------------------------------------------------------------------
b4+473a2c2+11368abc2-1823b2c2+4819ac3-10713bc3+7530c4-10508b3d-4318a2cd-
------------------------------------------------------------------------
10641abcd+10827b2cd-15407ac2d+9563bc2d-5255c3d+12557a2d2-14472abd2-
------------------------------------------------------------------------
1909b2d2-4946acd2-15532bcd2+11903c2d2-15800ad3+15771bd3+3101cd3+9073d4-
------------------------------------------------------------------------
15711b3e+6888a2ce+7350abce+14b2ce-8458ac2e+10955bc2e-3395c3e-6752a2de-
------------------------------------------------------------------------
10118abde-9078b2de-52acde-11770bcde+8963c2de+6867ad2e+6951bd2e-8325cd2e+
------------------------------------------------------------------------
9322d3e-9965a2e2-2020abe2+1055b2e2-3625ace2-10463bce2+12845c2e2+7315ade2
------------------------------------------------------------------------
+4639bde2-4158cde2+2933d2e2-641ae3+8049be3+12055ce3+7642de3+14065e4
------------------------------------------------------------------------
abc3-10362b2c3-11376ac4+5560bc4+13238c5-2058a2c2d-14103abc2d-13939b2c2d-
------------------------------------------------------------------------
6364ac3d+8127bc3d-10444c4d+6995b3d2-1649a2cd2+8632abcd2-2473b2cd2-
------------------------------------------------------------------------
14153ac2d2+15100bc2d2+7016c3d2-10482a2d3+12987abd3-6812b2d3-3729acd3+
------------------------------------------------------------------------
3459bcd3+13022c2d3-9171ad4-7794bd4+13442cd4-15549d5-7525a2c2e+3850abc2e+
------------------------------------------------------------------------
3181b2c2e+9389ac3e-4309bc3e-1142c4e+2617b3de-14903a2cde+8101abcde-
------------------------------------------------------------------------
5136b2cde-4714ac2de+8477bc2de-5616c3de-11437a2d2e-1803abd2e+2067b2d2e+
------------------------------------------------------------------------
1875acd2e-7069bcd2e-11595c2d2e-2563ad3e-8007bd3e+13569cd3e-13989d4e-
------------------------------------------------------------------------
14787b3e2-15315a2ce2+14608abce2-8008b2ce2+13241ac2e2+1077bc2e2-12881c3e2
------------------------------------------------------------------------
-6051a2de2-11949abde2+2829b2de2-13276acde2+8205bcde2-14197c2de2+
------------------------------------------------------------------------
4500ad2e2+9857bd2e2+8225cd2e2-2897d3e2+4660a2e3-4659abe3+13657b2e3-
------------------------------------------------------------------------
2927ace3-2217bce3+15004c2e3-10151ade3-11286bde3+8052cde3+4493d2e3+
------------------------------------------------------------------------
1688ae4+10601be4+4516ce4+15478de4+3679e5
------------------------------------------------------------------------
a2c3+26b2c3+6991ac4+13266bc4-15731c5-3824a2c2d+13976abc2d-5705b2c2d+
------------------------------------------------------------------------
4691ac3d-10241bc3d+1908c4d-9276b3d2+3236a2cd2+10638abcd2+3175b2cd2+
------------------------------------------------------------------------
4194ac2d2+4142bc2d2-4637c3d2+9827a2d3-9923abd3-7175b2d3-2344acd3+
------------------------------------------------------------------------
10241bcd3-10282c2d3-13553ad4+10828bd4+15102cd4-6094d5-12982a2c2e+
------------------------------------------------------------------------
12387abc2e+5290b2c2e-14851ac3e+3262bc3e+4592c4e-847b3de+3844a2cde-
------------------------------------------------------------------------
1304abcde+13993b2cde-7652ac2de-12466bc2de+15315c3de-7312a2d2e-9369abd2e-
------------------------------------------------------------------------
15654b2d2e-3909acd2e+5051bcd2e-12763c2d2e+3998ad3e-2323bd3e-2623cd3e+
------------------------------------------------------------------------
5561d4e+6270b3e2+4534a2ce2+8352abce2+13037b2ce2+8431ac2e2-12079bc2e2+
------------------------------------------------------------------------
12110c3e2+14548a2de2-12006abde2-15407b2de2-1249acde2-1593bcde2-3215c2de2
------------------------------------------------------------------------
+8617ad2e2+9979bd2e2+12839cd2e2-6745d3e2+12428a2e3-15260abe3+9865b2e3+
------------------------------------------------------------------------
3135ace3-3197bce3+13524c2e3-10942ade3+7721bde3+11340cde3+7629d2e3-
------------------------------------------------------------------------
13113ae4-11053be4-12387ce4-6401de4+340e5 |
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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